Cremona's table of elliptic curves

7410 = 2 · 3 · 5 · 13 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 13+ 19+	Signs for the Atkin-Lehner involutions
Class	7410s	Isogeny class
Conductor	7410	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	379392000 = 212 · 3 · 53 · 13 · 19	Discriminant
Eigenvalues	2- 3- 5+  0 -4 13+  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1951,-33319]	[a1,a2,a3,a4,a6]
Generators	[118:1117:1]	Generators of the group modulo torsion
j	821314391438449/379392000	j-invariant
L	6.7207248882931	L(r)(E,1)/r!
Ω	0.71836657764526	Real period
R	3.1185215169313	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	59280z1 22230r1 37050i1 96330bq1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 7410s1

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
-	-	+	0	-4	+	2	+	-8	2	8	-6	2	-8	4	-6	0	6	-16	0	-10	-4	4	18	-14

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Quadratic twists for elliptic curve 7410s1

-4	-3	5	13
59280z1	22230r1	37050i1	96330bq1

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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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