Atkin-Lehner |
2+ 3- 7- 11- 29- |
Signs for the Atkin-Lehner involutions |
Class |
13398u |
Isogeny class |
Conductor |
13398 |
Conductor |
∏ cp |
432 |
Product of Tamagawa factors cp |
deg |
103680 |
Modular degree for the optimal curve |
Δ |
-11203817351489532 = -1 · 22 · 33 · 74 · 116 · 293 |
Discriminant |
Eigenvalues |
2+ 3- 0 7- 11- 2 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-29761,-5465056] |
[a1,a2,a3,a4,a6] |
Generators |
[294:3202:1] |
Generators of the group modulo torsion |
j |
-2915045208415887625/11203817351489532 |
j-invariant |
L |
4.6720197243213 |
L(r)(E,1)/r! |
Ω |
0.16615116965074 |
Real period |
R |
2.3432575157019 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
6 |
Number of elements in the torsion subgroup |
Twists |
107184bk1 40194bs1 93786v1 |
Quadratic twists by: -4 -3 -7 |