Cremona's table of elliptic curves

7310 = 2 · 5 · 17 · 43

Field	Data	Notes
Atkin-Lehner	2+ 5+ 17+ 43+	Signs for the Atkin-Lehner involutions
Class	7310a	Isogeny class
Conductor	7310	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	3888	Modular degree for the optimal curve
Δ	540823040 = 29 · 5 · 173 · 43	Discriminant
Eigenvalues	2+  0 5+  1 -4  5 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-440,-3264]	[a1,a2,a3,a4,a6]
Generators	[-13:18:1]	Generators of the group modulo torsion
j	9432717529689/540823040	j-invariant
L	2.6763238539468	L(r)(E,1)/r!
Ω	1.0460237035636	Real period
R	2.5585690313032	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	58480d1 65790co1 36550x1 124270j1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 7310a1

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	+	1	-4	5	+	-8	8	4	-3	7	2	+	3	7	3	-10	0	6	4	0	12	0	-11

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Quadratic twists for elliptic curve 7310a1

-4	-3	5	17
58480d1	65790co1	36550x1	124270j1

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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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