Cremona's table of elliptic curves

623 = 7 · 89

Field	Data	Notes
Atkin-Lehner	7- 89-	Signs for the Atkin-Lehner involutions
Class	623a	Isogeny class
Conductor	623	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-10470761 = -1 · 76 · 89	Discriminant
Eigenvalues	1 -1  1 7- -4  2 -3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,28,157]	[a1,a2,a3,a4,a6]
Generators	[12:43:1]	Generators of the group modulo torsion
j	2294744759/10470761	j-invariant
L	2.2881851242035	L(r)(E,1)/r!
Ω	1.6365441157631	Real period
R	0.23303019068901	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	9968f1 39872q1 5607d1 15575e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 623a1

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	-1	1	-	-4	2	-3	-5	5	-6	-9	-8	-6	11	6	9	-4	-6	-6	-2	-11	12	12	-	3

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Quadratic twists for elliptic curve 623a1

-4	8	-3	5	-7	-11	13	89
9968f1	39872q1	5607d1	15575e1	4361a1	75383b1	105287b1	55447a1

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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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