Cremona's table of elliptic curves

2821 = 7 · 13 · 31

Field	Data	Notes
Atkin-Lehner	7+ 13+ 31+	Signs for the Atkin-Lehner involutions
Class	2821a	Isogeny class
Conductor	2821	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	232	Modular degree for the optimal curve
Δ	-19747 = -1 · 72 · 13 · 31	Discriminant
Eigenvalues	2  0  2 7+ -3 13+ -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,1,-7]	[a1,a2,a3,a4,a6]
Generators	[18:17:8]	Generators of the group modulo torsion
j	110592/19747	j-invariant
L	6.1834071259451	L(r)(E,1)/r!
Ω	1.8168744527824	Real period
R	1.7016605402964	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	45136h1 25389c1 70525m1 19747d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2821a1

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
2	0	2	+	-3	+	-2	-8	4	-4	+	-3	12	-8	6	12	4	2	-10	6	-1	-4	-8	3	-8

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Quadratic twists for elliptic curve 2821a1

-4	-3	5	-7	13	-31
45136h1	25389c1	70525m1	19747d1	36673b1	87451a1

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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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