Cremona's table of elliptic curves

2623 = 43 · 61

Field	Data	Notes
Atkin-Lehner	43+ 61-	Signs for the Atkin-Lehner involutions
Class	2623a	Isogeny class
Conductor	2623	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	816	Modular degree for the optimal curve
Δ	-419687869 = -1 · 432 · 613	Discriminant
Eigenvalues	1 -2 -1 -3 -3  1 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-144,1175]	[a1,a2,a3,a4,a6]
Generators	[-7:46:1] [17:52:1]	Generators of the group modulo torsion
j	-326940373369/419687869	j-invariant
L	3.2768774616091	L(r)(E,1)/r!
Ω	1.5162152905953	Real period
R	0.36020362476821	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	41968e1 23607e1 65575c1 128527c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2623a1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
1	-2	-1	-3	-3	1	-6	-2	-7	-6	-4	-6	5	+	4	-8	3	-	3	-4	11	-11	0	2	-2

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Quadratic twists for elliptic curve 2623a1

-4	-3	5	-7	-43
41968e1	23607e1	65575c1	128527c1	112789a1

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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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