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	2261d	Isogeny class
Conductor	2261	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-38000627 = -1 · 76 · 17 · 19	Discriminant
Eigenvalues	0  1  0 7-  0  2 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,37,-272]	[a1,a2,a3,a4,a6]
Generators	[1308:9244:27]	Generators of the group modulo torsion
j	5451776000/38000627	j-invariant
L	3.0955650760797	L(r)(E,1)/r!
Ω	1.0216657268157	Real period
R	4.5448794965374	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	36176l1 20349k1 56525j1 15827h1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2261d1

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
0	1	0	-	0	2	+	-	-6	3	-7	2	6	-1	3	0	-12	2	8	-12	-16	-16	-9	6	-13

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Quadratic twists for elliptic curve 2261d1

-4	-3	5	-7	17	-19
36176l1	20349k1	56525j1	15827h1	38437a1	42959h1

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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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