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	2961d	Isogeny class
Conductor	2961	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	6391522809 = 310 · 72 · 472	Discriminant
Eigenvalues	1 3- -2 7+  0  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-603,4360]	[a1,a2,a3,a4,a6]
j	33293019313/8767521	j-invariant
L	1.25080453694	L(r)(E,1)/r!
Ω	1.25080453694	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	47376bv2 987b2 74025v2 20727p2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2961d2

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	-	-2	+	0	2	-2	-4	4	-6	0	6	-6	8	+	10	4	6	8	-16	14	0	12	-2	18

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Quadratic twists for elliptic curve 2961d2

-4	-3	5	-7
47376bv2	987b2	74025v2	20727p2

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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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