Cremona's table of elliptic curves

Curve 52416w1

52416 = 26 · 32 · 7 · 13



Data for elliptic curve 52416w1

Field Data Notes
Atkin-Lehner 2+ 3+ 7- 13+ Signs for the Atkin-Lehner involutions
Class 52416w Isogeny class
Conductor 52416 Conductor
∏ cp 24 Product of Tamagawa factors cp
deg 55296 Modular degree for the optimal curve
Δ -252482420736 = -1 · 221 · 33 · 73 · 13 Discriminant
Eigenvalues 2+ 3+ -3 7- -3 13+ -3 -5 Hecke eigenvalues for primes up to 20
Equation [0,0,0,1236,17456] [a1,a2,a3,a4,a6]
Generators [-10:64:1] [-8:84:1] Generators of the group modulo torsion
j 29503629/35672 j-invariant
L 8.2003328352927 L(r)(E,1)/r!
Ω 0.65900291635484 Real period
R 0.51848106635675 Regulator
r 2 Rank of the group of rational points
S 0.99999999999999 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 52416dr1 1638n1 52416u2 Quadratic twists by: -4 8 -3


Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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