Cremona's table of elliptic curves

Curve 53312by1

53312 = 26 · 72 · 17



Data for elliptic curve 53312by1

Field Data Notes
Atkin-Lehner 2- 7- 17- Signs for the Atkin-Lehner involutions
Class 53312by Isogeny class
Conductor 53312 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 9216 Modular degree for the optimal curve
Δ -13647872 = -1 · 214 · 72 · 17 Discriminant
Eigenvalues 2-  1  0 7- -5 -5 17-  6 Hecke eigenvalues for primes up to 20
Equation [0,1,0,47,-113] [a1,a2,a3,a4,a6]
Generators [3:8:1] [69:580:1] Generators of the group modulo torsion
j 14000/17 j-invariant
L 10.761170101556 L(r)(E,1)/r!
Ω 1.1978939966148 Real period
R 2.245851914269 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 53312u1 13328s1 53312bi1 Quadratic twists by: -4 8 -7


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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