Atkin-Lehner |
2+ 5+ 7- 13- 17- |
Signs for the Atkin-Lehner involutions |
Class |
77350q |
Isogeny class |
Conductor |
77350 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
233472 |
Modular degree for the optimal curve |
Δ |
11275696250000 = 24 · 57 · 74 · 13 · 172 |
Discriminant |
Eigenvalues |
2+ -2 5+ 7- 2 13- 17- -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-8151,-233302] |
[a1,a2,a3,a4,a6] |
Generators |
[-1311:6592:27] [-68:121:1] |
Generators of the group modulo torsion |
j |
3832302404449/721644560 |
j-invariant |
L |
6.1571522975626 |
L(r)(E,1)/r! |
Ω |
0.50901306216499 |
Real period |
R |
0.75601599880451 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000012 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
15470j1 |
Quadratic twists by: 5 |