Cremona's table of elliptic curves

Curve 6314a1

6314 = 2 · 7 · 11 · 41



Data for elliptic curve 6314a1

Field Data Notes
Atkin-Lehner 2+ 7+ 11+ 41+ Signs for the Atkin-Lehner involutions
Class 6314a Isogeny class
Conductor 6314 Conductor
∏ cp 2 Product of Tamagawa factors cp
deg 1728 Modular degree for the optimal curve
Δ 13612984 = 23 · 73 · 112 · 41 Discriminant
Eigenvalues 2+  1 -3 7+ 11+  0 -1  4 Hecke eigenvalues for primes up to 20
Equation [1,0,1,-85,-248] [a1,a2,a3,a4,a6]
Generators [-4:7:1] Generators of the group modulo torsion
j 66775173193/13612984 j-invariant
L 2.576005502154 L(r)(E,1)/r!
Ω 1.5970942092764 Real period
R 0.80646635846271 Regulator
r 1 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 50512m1 56826z1 44198k1 69454x1 Quadratic twists by: -4 -3 -7 -11


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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