Cremona's table of elliptic curves

Curve 69440f1

69440 = 26 · 5 · 7 · 31



Data for elliptic curve 69440f1

Field Data Notes
Atkin-Lehner 2+ 5+ 7+ 31+ Signs for the Atkin-Lehner involutions
Class 69440f Isogeny class
Conductor 69440 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 138240 Modular degree for the optimal curve
Δ 445980344320 = 223 · 5 · 73 · 31 Discriminant
Eigenvalues 2+ -3 5+ 7+  1  1  6 -3 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-7948,270832] [a1,a2,a3,a4,a6]
Generators [62:128:1] Generators of the group modulo torsion
j 211815318681/1701280 j-invariant
L 3.1644372117959 L(r)(E,1)/r!
Ω 0.94410116971073 Real period
R 0.83794971186479 Regulator
r 1 Rank of the group of rational points
S 0.99999999977078 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 69440da1 2170d1 Quadratic twists by: -4 8


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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