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
deg	832	Modular degree for the optimal curve
Δ	14734937 = 74 · 17 · 192	Discriminant
Eigenvalues	-1  2 -2 7+  0  2 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-844,-9788]	[a1,a2,a3,a4,a6]
Generators	[966:1831:27]	Generators of the group modulo torsion
j	66494115285697/14734937	j-invariant
L	2.434749686352	L(r)(E,1)/r!
Ω	0.8857619865966	Real period
R	2.7487628992831	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	36176y1 20349f1 56525r1 15827l1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2261a1

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 2261a1

-4	-3	5	-7	17	-19
36176y1	20349f1	56525r1	15827l1	38437e1	42959e1

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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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