Atkin-Lehner |
2+ 31- 61- |
Signs for the Atkin-Lehner involutions |
Class |
60512d |
Isogeny class |
Conductor |
60512 |
Conductor |
∏ cp |
30 |
Product of Tamagawa factors cp |
deg |
304320 |
Modular degree for the optimal curve |
Δ |
-26616927531544576 = -1 · 212 · 315 · 613 |
Discriminant |
Eigenvalues |
2+ -2 1 2 3 0 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-65085,-10143893] |
[a1,a2,a3,a4,a6] |
Generators |
[2141:98332:1] |
Generators of the group modulo torsion |
j |
-7444116555337216/6498273323131 |
j-invariant |
L |
5.2524238833017 |
L(r)(E,1)/r! |
Ω |
0.14418317754114 |
Real period |
R |
1.2142941991445 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000436 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
60512e1 121024i1 |
Quadratic twists by: -4 8 |