Cremona's table of elliptic curves

2982 = 2 · 3 · 7 · 71

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 71-	Signs for the Atkin-Lehner involutions
Class	2982b	Isogeny class
Conductor	2982	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4480	Modular degree for the optimal curve
Δ	-23373536256 = -1 · 210 · 38 · 72 · 71	Discriminant
Eigenvalues	2+ 3+ -2 7- -6  4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-791,10965]	[a1,a2,a3,a4,a6]
Generators	[-2:113:1]	Generators of the group modulo torsion
j	-54841681585657/23373536256	j-invariant
L	1.8567163977783	L(r)(E,1)/r!
Ω	1.1248557439114	Real period
R	0.82531311584989	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	23856x1 95424be1 8946w1 74550dg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2982b1

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	-	-6	4	6	-4	4	-10	0	10	-2	8	12	-12	10	-8	-2	-	-10	16	-8	-18	-10

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Quadratic twists for elliptic curve 2982b1

-4	8	-3	5	-7
23856x1	95424be1	8946w1	74550dg1	20874r1

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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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