Cremona's table of elliptic curves

7921 = 89²

Field	Data	Notes
Atkin-Lehner	89+	Signs for the Atkin-Lehner involutions
Class	7921a	Isogeny class
Conductor	7921	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	19800	Modular degree for the optimal curve
Δ	44231334895529 = 897	Discriminant
Eigenvalues	1 -2 -2 -2 -4 -2  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-12047,394725]	[a1,a2,a3,a4,a6]
Generators	[-27181:330259:343]	Generators of the group modulo torsion
j	389017/89	j-invariant
L	2.0248121297009	L(r)(E,1)/r!
Ω	0.60305604148142	Real period
R	3.3575853493266	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	126736h1 71289e1 89b2	Quadratic twists by: -4 -3 89

Hecke Eigenvalues for elliptic curve 7921a1

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	-2	-2	-4	-2	6	2	-2	6	-6	-10	6	-2	12	-6	10	6	12	4	10	-12	6	+	-18

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Quadratic twists for elliptic curve 7921a1

-4	-3	89
126736h1	71289e1	89b2

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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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