Atkin-Lehner |
2+ 3+ 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
122304ca |
Isogeny class |
Conductor |
122304 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
11612160 |
Modular degree for the optimal curve |
Δ |
1.7323550277773E+20 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7- -4 13- -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-116963457,-486842253183] |
[a1,a2,a3,a4,a6] |
Generators |
[9936985729867328060707678782995539642775:-1713362979132345926589732576630618789853696:295409494634088869140933622152984375] |
Generators of the group modulo torsion |
j |
16728308209329751/16376256 |
j-invariant |
L |
5.6855619331489 |
L(r)(E,1)/r! |
Ω |
0.045907858133952 |
Real period |
R |
61.923624063205 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000063109 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
122304ih1 3822bd1 122304dm1 |
Quadratic twists by: -4 8 -7 |