Atkin-Lehner |
3+ 5- 13+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
30225p |
Isogeny class |
Conductor |
30225 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
287232 |
Modular degree for the optimal curve |
Δ |
98027724673125 = 311 · 54 · 134 · 31 |
Discriminant |
Eigenvalues |
-2 3+ 5- -4 -5 13+ 7 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-31208,-2057482] |
[a1,a2,a3,a4,a6] |
Generators |
[-89:84:1] |
Generators of the group modulo torsion |
j |
5378428787200000/156844359477 |
j-invariant |
L |
1.3788073584234 |
L(r)(E,1)/r! |
Ω |
0.35983733966941 |
Real period |
R |
1.9158758783762 |
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 |
90675bu1 30225z1 |
Quadratic twists by: -3 5 |