Cremona's table of elliptic curves

Curve 6909i1

6909 = 3 · 72 · 47



Data for elliptic curve 6909i1

Field Data Notes
Atkin-Lehner 3- 7- 47+ Signs for the Atkin-Lehner involutions
Class 6909i Isogeny class
Conductor 6909 Conductor
∏ cp 24 Product of Tamagawa factors cp
deg 3456 Modular degree for the optimal curve
Δ -4031007687 = -1 · 36 · 76 · 47 Discriminant
Eigenvalues -1 3-  0 7-  0 -6  6 -2 Hecke eigenvalues for primes up to 20
Equation [1,0,0,-393,4248] [a1,a2,a3,a4,a6]
Generators [-3:75:1] Generators of the group modulo torsion
j -57066625/34263 j-invariant
L 3.0355853441174 L(r)(E,1)/r!
Ω 1.2877571163343 Real period
R 0.392877573161 Regulator
r 1 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 110544cf1 20727o1 141b1 Quadratic twists by: -4 -3 -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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