Atkin-Lehner |
3- 5+ 11+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
18315i |
Isogeny class |
Conductor |
18315 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
491520 |
Modular degree for the optimal curve |
Δ |
4741882457476811625 = 314 · 53 · 118 · 37 |
Discriminant |
Eigenvalues |
1 3- 5+ 0 11+ -2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-5733540,-5281766325] |
[a1,a2,a3,a4,a6] |
Generators |
[37981899397744381575236513612686:3228426666955160230516111740648153:4689546740777640266586605467] |
Generators of the group modulo torsion |
j |
28593331973977048971841/6504639859364625 |
j-invariant |
L |
5.0377224416285 |
L(r)(E,1)/r! |
Ω |
0.097566284842273 |
Real period |
R |
51.633845131774 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6105j1 91575s1 |
Quadratic twists by: -3 5 |