Cremona's table of elliptic curves

2261 = 7 · 17 · 19

Field	Data	Notes
Atkin-Lehner	7+ 17+ 19+	Signs for the Atkin-Lehner involutions
Class	2261a	Isogeny class
Conductor	2261	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-31654522291 = -1 · 78 · 172 · 19	Discriminant
Eigenvalues	-1  2 -2 7+  0  2 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-749,-11954]	[a1,a2,a3,a4,a6]
Generators	[989:30615:1]	Generators of the group modulo torsion
j	-46473502468177/31654522291	j-invariant
L	2.434749686352	L(r)(E,1)/r!
Ω	0.4428809932983	Real period
R	5.4975257985662	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	36176y2 20349f2 56525r2 15827l2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2261a2

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

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Quadratic twists for elliptic curve 2261a2

-4	-3	5	-7	17	-19
36176y2	20349f2	56525r2	15827l2	38437e2	42959e2

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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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