Atkin-Lehner |
2+ 3+ 23- 37- |
Signs for the Atkin-Lehner involutions |
Class |
15318c |
Isogeny class |
Conductor |
15318 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
6912 |
Modular degree for the optimal curve |
Δ |
-48619332 = -1 · 22 · 33 · 233 · 37 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -1 0 -4 0 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1227,16857] |
[a1,a2,a3,a4,a6] |
Generators |
[-27:186:1] |
Generators of the group modulo torsion |
j |
-7569944872875/1800716 |
j-invariant |
L |
3.3614630346136 |
L(r)(E,1)/r! |
Ω |
1.9579594672693 |
Real period |
R |
1.2876146407036 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
122544p1 15318i2 |
Quadratic twists by: -4 -3 |