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	2982a	Isogeny class
Conductor	2982	Conductor
∏ cp	7	Product of Tamagawa factors cp
deg	4480	Modular degree for the optimal curve
Δ	-28417174758 = -1 · 2 · 35 · 77 · 71	Discriminant
Eigenvalues	2+ 3+  0 7-  2  4 -6  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-8605,303787]	[a1,a2,a3,a4,a6]
Generators	[39:152:1]	Generators of the group modulo torsion
j	-70478263190049625/28417174758	j-invariant
L	2.2735689974462	L(r)(E,1)/r!
Ω	1.16156702049	Real period
R	0.27961845105306	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	23856w1 95424bd1 8946u1 74550df1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2982a1

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
+	+	0	-	2	4	-6	1	-7	1	-7	0	-12	6	8	6	-3	14	-7	-	-14	-5	-14	-7	-1

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Quadratic twists for elliptic curve 2982a1

-4	8	-3	5	-7
23856w1	95424bd1	8946u1	74550df1	20874q1

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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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