Cremona's table of elliptic curves

Curve 6409c1

6409 = 13 · 17 · 29



Data for elliptic curve 6409c1

Field Data Notes
Atkin-Lehner 13+ 17- 29+ Signs for the Atkin-Lehner involutions
Class 6409c Isogeny class
Conductor 6409 Conductor
∏ cp 1 Product of Tamagawa factors cp
deg 1872 Modular degree for the optimal curve
Δ -910904761 = -1 · 133 · 17 · 293 Discriminant
Eigenvalues -1  0  1 -2  3 13+ 17- -4 Hecke eigenvalues for primes up to 20
Equation [1,-1,1,-172,-1648] [a1,a2,a3,a4,a6]
j -559679941521/910904761 j-invariant
L 0.62427850872236 L(r)(E,1)/r!
Ω 0.62427850872236 Real period
R 1 Regulator
r 0 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 102544e1 57681e1 83317c1 108953d1 Quadratic twists by: -4 -3 13 17


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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