Cremona's table of elliptic curves

Curve 7869d1

7869 = 3 · 43 · 61



Data for elliptic curve 7869d1

Field Data Notes
Atkin-Lehner 3+ 43- 61- Signs for the Atkin-Lehner involutions
Class 7869d Isogeny class
Conductor 7869 Conductor
∏ cp 20 Product of Tamagawa factors cp
deg 36720 Modular degree for the optimal curve
Δ -398776425557787 = -1 · 36 · 435 · 612 Discriminant
Eigenvalues -2 3+  2  2 -1 -5 -3  2 Hecke eigenvalues for primes up to 20
Equation [0,-1,1,18388,-51502] [a1,a2,a3,a4,a6]
Generators [1073:35410:1] Generators of the group modulo torsion
j 687548879731699712/398776425557787 j-invariant
L 2.0605494593071 L(r)(E,1)/r!
Ω 0.3164048147143 Real period
R 0.32561916941241 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 125904p1 23607h1 Quadratic twists by: -4 -3


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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