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	7475d	Isogeny class
Conductor	7475	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	8640	Modular degree for the optimal curve
Δ	12357109375 = 57 · 13 · 233	Discriminant
Eigenvalues	1 -1 5+  1  2 13- -5  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-27525,1746250]	[a1,a2,a3,a4,a6]
Generators	[94:-24:1]	Generators of the group modulo torsion
j	147608144916049/790855	j-invariant
L	4.0551094360071	L(r)(E,1)/r!
Ω	1.1234668566539	Real period
R	0.60157677875857	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	119600bd1 67275o1 1495a1 97175j1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 7475d1

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	2	-	-5	0	-	-1	5	8	0	8	2	-2	-3	-4	-5	-12	3	-15	1	-13	14

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Quadratic twists for elliptic curve 7475d1

-4	-3	5	13
119600bd1	67275o1	1495a1	97175j1

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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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