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	2261c	Isogeny class
Conductor	2261	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	39994829 = 73 · 17 · 193	Discriminant
Eigenvalues	2  0  1 7+ -6  1 17- 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-227,-1281]	[a1,a2,a3,a4,a6]
Generators	[-78:15:8]	Generators of the group modulo torsion
j	1293603803136/39994829	j-invariant
L	5.5385353367704	L(r)(E,1)/r!
Ω	1.2322958119763	Real period
R	1.4981617462688	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	36176bc1 20349e1 56525p1 15827c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2261c1

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	0	1	+	-6	1	-	-	-2	3	-2	7	-12	-8	0	0	3	-1	-8	8	9	-3	8	1	2

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Quadratic twists for elliptic curve 2261c1

-4	-3	5	-7	17	-19
36176bc1	20349e1	56525p1	15827c1	38437i1	42959g1

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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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