Cremona's table of elliptic curves

Curve 6786b1

6786 = 2 · 32 · 13 · 29



Data for elliptic curve 6786b1

Field Data Notes
Atkin-Lehner 2+ 3+ 13- 29- Signs for the Atkin-Lehner involutions
Class 6786b Isogeny class
Conductor 6786 Conductor
∏ cp 8 Product of Tamagawa factors cp
deg 8064 Modular degree for the optimal curve
Δ -2086760797056 = -1 · 27 · 39 · 134 · 29 Discriminant
Eigenvalues 2+ 3+  1 -1  0 13- -1  1 Hecke eigenvalues for primes up to 20
Equation [1,-1,0,-3174,98612] [a1,a2,a3,a4,a6]
Generators [37:157:1] Generators of the group modulo torsion
j -179692582707/106018432 j-invariant
L 3.1680489044331 L(r)(E,1)/r!
Ω 0.76544455701293 Real period
R 0.51735440460835 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 54288bb1 6786i1 88218bp1 Quadratic twists by: -4 -3 13


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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