Atkin-Lehner |
2+ 3- 37- |
Signs for the Atkin-Lehner involutions |
Class |
21312u |
Isogeny class |
Conductor |
21312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
4608 |
Modular degree for the optimal curve |
Δ |
-63872064 = -1 · 26 · 36 · 372 |
Discriminant |
Eigenvalues |
2+ 3- 2 4 0 -2 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-99,-540] |
[a1,a2,a3,a4,a6] |
Generators |
[386862:4581585:2744] |
Generators of the group modulo torsion |
j |
-2299968/1369 |
j-invariant |
L |
6.7559411206193 |
L(r)(E,1)/r! |
Ω |
0.73668131134485 |
Real period |
R |
9.1707784853209 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
21312v1 10656e2 2368d1 |
Quadratic twists by: -4 8 -3 |