Cremona's table of elliptic curves

Curve 51336g1

51336 = 23 · 32 · 23 · 31



Data for elliptic curve 51336g1

Field Data Notes
Atkin-Lehner 2+ 3- 23+ 31+ Signs for the Atkin-Lehner involutions
Class 51336g Isogeny class
Conductor 51336 Conductor
∏ cp 16 Product of Tamagawa factors cp
deg 368640 Modular degree for the optimal curve
Δ -1590749947844352 = -1 · 28 · 312 · 233 · 312 Discriminant
Eigenvalues 2+ 3-  4  0  4 -2  6 -8 Hecke eigenvalues for primes up to 20
Equation [0,0,0,26457,-968870] [a1,a2,a3,a4,a6]
j 10974329876144/8523823023 j-invariant
L 4.2348082616121 L(r)(E,1)/r!
Ω 0.26467551635385 Real period
R 1 Regulator
r 0 Rank of the group of rational points
S 4 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 102672t1 17112n1 Quadratic twists by: -4 -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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