Cremona's table of elliptic curves

Curve 4047a2

4047 = 3 · 19 · 71



Data for elliptic curve 4047a2

Field Data Notes
Atkin-Lehner 3- 19+ 71+ Signs for the Atkin-Lehner involutions
Class 4047a Isogeny class
Conductor 4047 Conductor
∏ cp 24 Product of Tamagawa factors cp
Δ 478915209369 = 36 · 194 · 712 Discriminant
Eigenvalues -1 3- -2 -4  4  6  6 19+ Hecke eigenvalues for primes up to 20
Equation [1,0,0,-3354,-67221] [a1,a2,a3,a4,a6]
j 4172736682666657/478915209369 j-invariant
L 0.94805749056202 L(r)(E,1)/r!
Ω 0.63203832704135 Real period
R 1 Regulator
r 0 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 4 Number of elements in the torsion subgroup
Twists 64752k2 12141f2 101175b2 76893d2 Quadratic twists by: -4 -3 5 -19


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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