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	2961h	Isogeny class
Conductor	2961	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	26880	Modular degree for the optimal curve
Δ	-2782018958505003 = -1 · 313 · 75 · 473	Discriminant
Eigenvalues	-2 3- -4 7+ -1 -2  3  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-18597,-2718954]	[a1,a2,a3,a4,a6]
Generators	[347:5710:1]	Generators of the group modulo torsion
j	-975719213461504/3816212563107	j-invariant
L	1.157737868322	L(r)(E,1)/r!
Ω	0.18672468140093	Real period
R	0.51668667992715	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	47376bn1 987d1 74025n1 20727m1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2961h1

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	-	-4	+	-1	-2	3	1	-3	2	-3	3	10	-10	-	6	-3	10	10	-6	15	-13	-3	-1	6

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Quadratic twists for elliptic curve 2961h1

-4	-3	5	-7
47376bn1	987d1	74025n1	20727m1

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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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