Cremona's table of elliptic curves

7600 = 2⁴ · 5² · 19

Field	Data	Notes
Atkin-Lehner	2+ 5+ 19+	Signs for the Atkin-Lehner involutions
Class	7600b	Isogeny class
Conductor	7600	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	11281250000 = 24 · 59 · 192	Discriminant
Eigenvalues	2+ -2 5+  0  4 -4  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-883,-9012]	[a1,a2,a3,a4,a6]
Generators	[68:500:1]	Generators of the group modulo torsion
j	304900096/45125	j-invariant
L	2.8765111044713	L(r)(E,1)/r!
Ω	0.88439755075801	Real period
R	1.6262545627845	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	3800h1 30400bu1 68400bg1 1520a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7600b1

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

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Quadratic twists for elliptic curve 7600b1

-4	8	-3	5
3800h1	30400bu1	68400bg1	1520a1

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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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