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Jul 16, 2022 at 21:53 comment added user471019 It's equation (2.8.10) in Cremona. There is an additional factor of $2$ there. By the way, Magma tells me that the $L$-ratio is $1/4$. (It depends on how you define $\Omega_E$.)
Jul 16, 2022 at 19:04 comment added Duality I'm confused. For $p=2$, the elliptic curve has good reduction, so the denominator is smaller than $3$ ? Which prime $p$ you take ?
Jul 16, 2022 at 18:23 comment added user471019 In Cremona's book (somewhere around §2.8?), there is a proof using modular symbols that $L(E,1)/\Omega_E$ is a rational number with denominator bounded by $(p+1)-a_p$ for $p$ a prime of good reduction. Hence, approximating that number to this precision will give it you exactly.
Jul 16, 2022 at 17:22 comment added Duality If we admit $L(E,1)=0.65551438837・・・$ and $Ω(E)=5.24411510858・・・$ , from this, can we say $L(E,1)/Ω(E)=1/8$ without using computer ?
Jul 16, 2022 at 17:19 history edited Michael Hardy CC BY-SA 4.0
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Jul 16, 2022 at 11:29 comment added Chris Wuthrich You can do so by using module symbols, as it is the value of the modular symbol (suitably normalised with respect to your period) evaluated at 0. See this question here for how this is done. Cremona's book is a good source for the basics of how to verify BSD for elliptic curves.
Jul 16, 2022 at 10:46 history edited Duality CC BY-SA 4.0
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Jul 16, 2022 at 8:25 history edited Daniele Tampieri CC BY-SA 4.0
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Jul 16, 2022 at 8:03 history edited Duality CC BY-SA 4.0
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Jul 16, 2022 at 7:33 history asked Duality CC BY-SA 4.0