We are searching for rank $8$ elliptic curves with the torsion subgroup $\mathbb{Z}/6$ using newly discovered families similar to Kihara's as described in

A. Dujella, J.C. Peral, P. Tadić,

Elliptic curves with torsion group $\mathbb{Z}/6\mathbb{Z}$, Glas. Mat. Ser. III 51 (2016), 321-333 doi:10.3336/gm.51.2.03, 1503.03667

and came across a curve

```
[0,1,0,-60313024735007362096072931339173916555726439220,3303762732437764940265112114690488828303891527290367159038723810320068]
```

Both Magma Calculator and mwrank (with $-b14$) return $7$ generators for this curve:

```
SetClassGroupBounds("GRH");
E:=EllipticCurve([0,1,0,-60313024735007362096072931339173916555726439220,3303762732437764940265112114690488828303891527290367159038723810320068]);
MordellWeilShaInformation(E);
Using model [ 0, 1, 0, -60313024735007362096072931339173916555726439220, 3303762732437764940265112114690488828303891527290367159038723810320068 ]
Torsion Subgroup = Z/6
The 2-Selmer group has rank 9
New point of infinite order (x = 5260000916960497219694209104164/9078169)
New point of infinite order (x = -146551684206472947976069)
New point of infinite order (x = -151681843950496144133344)
New point of infinite order (x = 211401387771733499670296)
New point of infinite order (x = 1521645572343712794396956)
New point of infinite order (x = 14998786693919437193768749863407/42159049)
New point of infinite order (x = 1185363853402839599279348827593704/4311629569)
After 2-descent:
7 <= Rank(E) <= 8
Sha(E)[2] <= (Z/2)^1
(Searched up to height 10000 on the 2-coverings.)
```

Both Magma and mwrank return $8$ for the upper bound on rank:

```
E:=EllipticCurve([0,1,0,-60313024735007362096072931339173916555726439220,3303762732437764940265112114690488828303891527290367159038723810320068]);
TwoPowerIsogenyDescentRankBound(E);
8 [ 3, 3, 3, 3, 3 ]
[ 7, 7, 7, 7, 7 ]
```

```
mwrank -v0 -p200 -s
[0,1,0,-60313024735007362096072931339173916555726439220,3303762732437764940265112114690488828303891527290367159038723810320068]
Version compiled on Oct 29 2018 at 22:35:09 by GCC 7.3.0
using NTL bigints and NTL real and complex multiprecision floating point
Enter curve: [0,1,0,-60313024735007362096072931339173916555726439220,3303762732437764940265112114690488828303891527290367159038723810320068]
Curve [0,1,0,-60313024735007362096072931339173916555726439220,3303762732437764940265112114690488828303891527290367159038723810320068] : selmer-rank = 9
upper bound on rank = 8
```

Considering parity, there should be one more generator on the curve.

Is there a way to find it?

We would greatly appreciate any hint leading to the discovery of the extra generator.

A bounty of $100$ will be offered for obtaining it.

Also, if you can compute an extra generator, your name will be published at the bottom of the page here: https://web.math.pmf.unizg.hr/~duje/tors/z6.html.

So far, we are unsuccsessful applying Zev Klagsbrun's approach.

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