Cremona's table of elliptic curves

118 = 2 · 59

Field	Data	Notes
Atkin-Lehner	2+ 59-	Signs for the Atkin-Lehner involutions
Class	118d	Isogeny class
Conductor	118	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	38	Modular degree for the optimal curve
Δ	-30932992 = -1 · 219 · 59	Discriminant
Eigenvalues	2+  2  2 -3  1  3 -1 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,56,-192]	[a1,a2,a3,a4,a6]
j	18884848247/30932992	j-invariant
L	1.0990077472008	L(r)(E,1)/r!
Ω	1.0990077472008	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	944g1 3776e1 1062i1 2950q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 118d1

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	2	-3	1	3	-1	-8	8	-4	-4	-1	5	-9	2	12	-	10	4	-15	10	11	-11	-6	14

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Quadratic twists for elliptic curve 118d1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	-59
944g1	3776e1	1062i1	2950q1	5782a1	14278i1	19942g1	34102i1	42598f1	62422d1	99238o1	113398c1	6962k1

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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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