Atkin-Lehner |
2+ 3+ 5- 11- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
12210j |
Isogeny class |
Conductor |
12210 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
83328 |
Modular degree for the optimal curve |
Δ |
9557472612188160 = 231 · 37 · 5 · 11 · 37 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -1 11- 1 -3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-56617,2158981] |
[a1,a2,a3,a4,a6] |
Generators |
[-300:99799:64] |
Generators of the group modulo torsion |
j |
20071334919501405721/9557472612188160 |
j-invariant |
L |
3.0285393063737 |
L(r)(E,1)/r! |
Ω |
0.36479415597486 |
Real period |
R |
8.3020499554889 |
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 |
97680cs1 36630bc1 61050cl1 |
Quadratic twists by: -4 -3 5 |