Cremona's table of elliptic curves

122 = 2 · 61

Field	Data	Notes
Atkin-Lehner	2+ 61+	Signs for the Atkin-Lehner involutions
Class	122a	Isogeny class
Conductor	122	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-976 = -1 · 24 · 61	Discriminant
Eigenvalues	2+ -2  1 -5 -3 -3  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,2,0]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	1685159/976	j-invariant
L	0.71686594671776	L(r)(E,1)/r!
Ω	2.9660992729099	Real period
R	0.12084321540837	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	976a1 3904b1 1098j1 3050f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 122a1

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	1	-5	-3	-3	0	0	5	6	0	-12	-3	-8	12	-2	-9	+	7	-16	-3	1	-12	12	2

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Quadratic twists for elliptic curve 122a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	61
976a1	3904b1	1098j1	3050f1	5978g1	14762i1	20618i1	35258d1	44042f1	64538d1	102602e1	117242d1	7442b1

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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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