Atkin-Lehner |
3+ 5+ 11+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
18315b |
Isogeny class |
Conductor |
18315 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
4631348390625 = 39 · 56 · 11 · 372 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 2 11+ 0 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-97013,11654092] |
[a1,a2,a3,a4,a6] |
Generators |
[613:13193:1] |
Generators of the group modulo torsion |
j |
5130007819771563/235296875 |
j-invariant |
L |
3.2406358041133 |
L(r)(E,1)/r! |
Ω |
0.72750497621795 |
Real period |
R |
2.2272258678973 |
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 |
18315f1 91575e1 |
Quadratic twists by: -3 5 |