Cremona's table of elliptic curves

760 = 2³ · 5 · 19

Field	Data	Notes
Atkin-Lehner	2+ 5- 19-	Signs for the Atkin-Lehner involutions
Class	760d	Isogeny class
Conductor	760	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	722000 = 24 · 53 · 192	Discriminant
Eigenvalues	2+ -2 5-  0 -4  4 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-35,58]	[a1,a2,a3,a4,a6]
Generators	[1:5:1]	Generators of the group modulo torsion
j	304900096/45125	j-invariant
L	1.7874773124556	L(r)(E,1)/r!
Ω	2.7369997770299	Real period
R	0.217693028629	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1520a1 6080b1 6840s1 3800h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 760d1

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	-	0	-4	4	-2	-	-4	-6	-8	-4	-2	4	-8	0	-8	2	-14	-8	6	-4	16	-18	-4

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Quadratic twists for elliptic curve 760d1

-4	8	-3	5	-7	-11	13	-19
1520a1	6080b1	6840s1	3800h1	37240b1	91960x1	128440n1	14440j1

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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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