Cremona's table of elliptic curves

2961 = 3² · 7 · 47

Field	Data	Notes
Atkin-Lehner	3- 7+ 47+	Signs for the Atkin-Lehner involutions
Class	2961f	Isogeny class
Conductor	2961	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	913074687 = 310 · 7 · 472	Discriminant
Eigenvalues	-1 3- -4 7+ -2  0 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-257,690]	[a1,a2,a3,a4,a6]
Generators	[-16:30:1] [-9:51:1]	Generators of the group modulo torsion
j	2565726409/1252503	j-invariant
L	2.3393190655468	L(r)(E,1)/r!
Ω	1.3982361536975	Real period
R	0.83652502453212	Regulator
r	2	Rank of the group of rational points
S	0.99999999999991	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	47376cb2 987a2 74025s2 20727s2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2961f2

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	-	-4	+	-2	0	-6	-4	-6	-6	-4	-10	0	6	+	-10	-12	10	-14	8	-4	-8	-12	-18	-14

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Quadratic twists for elliptic curve 2961f2

-4	-3	5	-7
47376cb2	987a2	74025s2	20727s2

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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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