Cremona's table of elliptic curves

7462 = 2 · 7 · 13 · 41

Field	Data	Notes
Atkin-Lehner	2+ 7+ 13+ 41-	Signs for the Atkin-Lehner involutions
Class	7462b	Isogeny class
Conductor	7462	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	9984	Modular degree for the optimal curve
Δ	3290344185856 = 213 · 73 · 134 · 41	Discriminant
Eigenvalues	2+  1 -1 7+  0 13+ -3  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-6724,-193982]	[a1,a2,a3,a4,a6]
j	33613518667426489/3290344185856	j-invariant
L	1.0610985156116	L(r)(E,1)/r!
Ω	0.53054925780579	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	59696s1 67158bj1 52234m1 97006o1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 7462b1

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	+	0	+	-3	4	6	3	5	-4	-	-1	-6	-1	10	-7	-4	-7	-2	1	-4	-9	3

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Quadratic twists for elliptic curve 7462b1

-4	-3	-7	13
59696s1	67158bj1	52234m1	97006o1

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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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