Atkin-Lehner |
7+ 19+ 73- |
Signs for the Atkin-Lehner involutions |
Class |
67963a |
Isogeny class |
Conductor |
67963 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
51408 |
Modular degree for the optimal curve |
Δ |
-151919800753 = -1 · 78 · 192 · 73 |
Discriminant |
Eigenvalues |
-1 -2 0 7+ -3 -4 -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,1322,-2955] |
[a1,a2,a3,a4,a6] |
Generators |
[53:439:1] [69:612:1] |
Generators of the group modulo torsion |
j |
44321375/26353 |
j-invariant |
L |
4.0571627863686 |
L(r)(E,1)/r! |
Ω |
0.60049934472311 |
Real period |
R |
1.1260525155774 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
67963g1 |
Quadratic twists by: -7 |