The curve is the fibre at T = 4/13 from curve #4220:
- A4(4/13) = −250530051225379351163799381830307 / 13⁸
- A6(4/13) = 1551614814321580263454294680252020288318239844190 / 13¹²
Integral model. The denominators are 13⁸ and 13¹². Scaling x and y by 13⁴ and 13⁶ clears them, which gives
y² = x³ − 250530051225379351163799381830307 x + 1551614814321580263454294680252020288318239844190.
Its minimal model is the record curve:
[1, 0, 1, −8528221325987577221628, 308163977335241285581239029798542]
Rank 18, proved: 18 independent points listed, matching the 2-descent upper bound. Torsion trivial.
Michael Rubinstein ·
Michael Rubinstein ·