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I should add that the full length program, for use with magma itself, not an online calculator website, had significant preprocessing in C++ as well as postprocessing. Maybe the most important thing missing is the reduction of forms according to the reduction scheme of Alexander Schiemann. As a result, you should have some method for deciding whether two (positive) forms are equivalent. This is a finite check, not difficult, but needs to be done. For example, the output (far below) gives $\langle 1,4,9,-4,0,0 \rangle$ insted of $\langle 1,4,9,4,0,0 \rangle.$ Also, magma prints some peculiar things when the power of $2$ dividing the discriminant is large. When you ask for the genus of the regular form $\langle 1,8,64,0,0,0 \rangle,$ it correctly says there are two spinor genera but types the same form in both, an obvious error. This error first came to light when Manjul Bhargava asked Kaplansky about genera of a single class. So, things should be checked with, for example, the mass formula. One simple check is that spinor genera of the same genus must have the same mass.

I should add that the full length program, for use with magma itself, not an online calculator website, had significant preprocessing in C++ as well as postprocessing. Maybe the most important thing missing is the reduction of forms according to the reduction scheme of Alexander Schiemann. As a result, you should have some method for deciding whether two (positive) forms are equivalent. This is a finite check, not difficult, but needs to be done. For example, the output (far below) gives $\langle 1,4,9,-4,0,0 \rangle$ insted of $\langle 1,4,9,4,0,0 \rangle.$ Also, magma prints some peculiar things when the power of $2$ dividing the discriminant is large. When you ask for the genus of the regular form $\langle 1,8,64,0,0,0 \rangle,$ it correctly says there are two spinor genera but types the same form in both, an obvious error. This error first came to light when Manjul Bhargava asked Kaplansky about genera of a single class. Jones and Pall (1939) gave the correct second form, in my notation $\langle 4,8,17,0,4,0 \rangle,$ but gave the wrong spinor exceptions, corrected by Schulze-Pillot. So, things should be checked with, for example, the mass formula. One simple check is that spinor genera of the same genus must have the same mass.

I should add that the full length program, for use with magma itself, not an online calculator website, had significant preprocessing in C++ as well as postprocessing. Maybe the most important thing missing is the reduction of forms according to the reduction scheme of Alexander Schiemann. As a result, you should have some method for deciding whether two (positive) forms are equivalent. This is a finite check, not difficult, but needs to be done. Also, magma prints some peculiar things when the power of $2$ dividing the discriminant is large. So, things should be checked with, for example the mass formula. One simple check is that spinor genera of the same genus must have the same mass.

I should add that the full length program, for use with magma itself, not an online calculator website, had significant preprocessing in C++ as well as postprocessing. Maybe the most important thing missing is the reduction of forms according to the reduction scheme of Alexander Schiemann. As a result, you should have some method for deciding whether two (positive) forms are equivalent. This is a finite check, not difficult, but needs to be done. For example, the output (far below) gives $\langle 1,4,9,-4,0,0 \rangle$ insted of $\langle 1,4,9,4,0,0 \rangle.$ Also, magma prints some peculiar things when the power of $2$ dividing the discriminant is large. When you ask for the genus of the regular form $\langle 1,8,64,0,0,0 \rangle,$ it correctly says there are two spinor genera but types the same form in both, an obvious error. This error first came to light when Manjul Bhargava asked Kaplansky about genera of a single class. So, things should be checked with, for example, the mass formula. One simple check is that spinor genera of the same genus must have the same mass.

I should add that the full length program, for use with magma itself, not an online calculator website, had significant preprocessing in C++ as well as postprocessing. Maybe the most important thing missing is the reduction of forms according to the reduction scheme of Alexander Schiemann. As a result, you should have some method for deciding whether two (positive) forms are equivalent. This is a finite check, not difficult, but needs to be done. Also, magma prints some peculiar things when the power of $2$ dividing the discriminant is large. So, things should be checked with, for example the mass formula. One simple check is that spinor genera of the same genus must have the same mass.