Cremona's table of elliptic curves

7475 = 5² · 13 · 23

Field	Data	Notes
Atkin-Lehner	5+ 13+ 23-	Signs for the Atkin-Lehner involutions
Class	7475b	Isogeny class
Conductor	7475	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	583984375 = 59 · 13 · 23	Discriminant
Eigenvalues	-1 -1 5+ -1 -6 13+  3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-313,1656]	[a1,a2,a3,a4,a6]
Generators	[-4:55:1] [20:52:1]	Generators of the group modulo torsion
j	217081801/37375	j-invariant
L	3.0294680243747	L(r)(E,1)/r!
Ω	1.5575568254325	Real period
R	0.48625320998043	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	119600m1 67275g1 1495d1 97175g1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 7475b1

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	+	-1	-6	+	3	-4	-	-1	-5	-4	-4	-12	-6	14	-13	8	-11	12	-3	-15	-9	-11	-6

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Quadratic twists for elliptic curve 7475b1

-4	-3	5	13
119600m1	67275g1	1495d1	97175g1

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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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