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	2261b	Isogeny class
Conductor	2261	Conductor
∏ cp	7	Product of Tamagawa factors cp
deg	13328	Modular degree for the optimal curve
Δ	6420699293790341 = 77 · 177 · 19	Discriminant
Eigenvalues	0 -2  3 7+ -4  3 17- 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-96339,10812429]	[a1,a2,a3,a4,a6]
Generators	[51:2456:1]	Generators of the group modulo torsion
j	98885957283487055872/6420699293790341	j-invariant
L	2.1236963952308	L(r)(E,1)/r!
Ω	0.41536801575731	Real period
R	0.73040096446893	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	36176be1 20349d1 56525o1 15827b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2261b1

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	-2	3	+	-4	3	-	-	0	-1	-4	-5	8	-8	4	-2	1	13	-4	-8	7	1	-2	-9	-6

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Quadratic twists for elliptic curve 2261b1

-4	-3	5	-7	17	-19
36176be1	20349d1	56525o1	15827b1	38437g1	42959f1

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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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