Atkin-Lehner |
2+ 3+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69312f |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
8171520 |
Modular degree for the optimal curve |
Δ |
4.7359932951671E+22 |
Discriminant |
Eigenvalues |
2+ 3+ -2 4 2 4 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-22342049,39283146273] |
[a1,a2,a3,a4,a6] |
Generators |
[-225970757151636959:-21422290266537724928:76014879491881] |
Generators of the group modulo torsion |
j |
14580432307/559872 |
j-invariant |
L |
5.98347599014 |
L(r)(E,1)/r! |
Ω |
0.11231173772236 |
Real period |
R |
26.637803454859 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998268 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69312de1 2166c1 69312bh1 |
Quadratic twists by: -4 8 -19 |