Cremona's table of elliptic curves

61 = Prime conductor

Field	Data	Notes
Atkin-Lehner	61+	Signs for the Atkin-Lehner involutions
Class	61a	Isogeny class
Conductor	61	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2	Modular degree for the optimal curve
Δ	-61 = Prime discriminant	Discriminant
Eigenvalues	-1 -2 -3  1 -5  1  4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2,1]	[a1,a2,a3,a4,a6]
Generators	[1:-1:1]	Generators of the group modulo torsion
j	-912673/61	j-invariant
L	0.48567365142658	L(r)(E,1)/r!
Ω	6.1331931483945	Real period
R	0.079187731362042	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	976b1 3904c1 549c1 1525a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 61a1

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	-3	1	-5	1	4	-4	-9	-6	0	8	5	-8	4	6	9	+	-7	-8	-11	3	4	-4	-14

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Quadratic twists for elliptic curve 61a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	61
976b1	3904c1	549c1	1525a1	2989d1	7381c1	10309a1	17629b1	22021a1	32269a1	51301b1	58621d1	83509b1	102541a1	112789b1	3721a1

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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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