Atkin-Lehner |
2+ 3+ 5- 37- |
Signs for the Atkin-Lehner involutions |
Class |
3330d |
Isogeny class |
Conductor |
3330 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
51840 |
Modular degree for the optimal curve |
Δ |
-436767073801920000 = -1 · 29 · 39 · 54 · 375 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -3 1 1 -1 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-560994,164964500] |
[a1,a2,a3,a4,a6] |
Generators |
[481:2257:1] |
Generators of the group modulo torsion |
j |
-991990479802737267/22190066240000 |
j-invariant |
L |
2.5568408262646 |
L(r)(E,1)/r! |
Ω |
0.29735250266021 |
Real period |
R |
0.21496715206617 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
26640ba1 106560c1 3330o1 16650bo1 |
Quadratic twists by: -4 8 -3 5 |