Cremona's table of elliptic curves

118 = 2 · 59

Field	Data	Notes
Atkin-Lehner	2- 59+	Signs for the Atkin-Lehner involutions
Class	118b	Isogeny class
Conductor	118	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	-60416 = -1 · 210 · 59	Discriminant
Eigenvalues	2- -1  1  3  2 -6 -2 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-25,39]	[a1,a2,a3,a4,a6]
j	-1732323601/60416	j-invariant
L	1.3953806318622	L(r)(E,1)/r!
Ω	3.4884515796555	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	944h1 3776f1 1062d1 2950a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 118b1

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	1	3	2	-6	-2	-5	4	-5	2	8	7	-6	-2	9	+	-8	-2	12	4	5	14	0	8

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Quadratic twists for elliptic curve 118b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	-59
944h1	3776f1	1062d1	2950a1	5782h1	14278a1	19942c1	34102m1	42598b1	62422f1	99238a1	113398e1	6962c1

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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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