Cremona's table of elliptic curves

118 = 2 · 59

Field	Data	Notes
Atkin-Lehner	2+ 59+	Signs for the Atkin-Lehner involutions
Class	118a	Isogeny class
Conductor	118	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4	Modular degree for the optimal curve
Δ	-236 = -1 · 22 · 59	Discriminant
Eigenvalues	2+ -1 -3 -1 -2 -2 -2  3	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,1,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	12167/236	j-invariant
L	0.73110830800221	L(r)(E,1)/r!
Ω	4.1584572189565	Real period
R	0.087906195676299	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	944i1 3776g1 1062l1 2950l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 118a1

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	-3	-1	-2	-2	-2	3	0	-1	10	-12	7	-6	-6	-11	+	-12	10	4	12	-15	-14	4	0

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Quadratic twists for elliptic curve 118a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	-59
944i1	3776g1	1062l1	2950l1	5782c1	14278f1	19942j1	34102e1	42598g1	62422b1	99238i1	113398a1	6962j1

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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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