Cremona's table of elliptic curves

7840 = 2⁵ · 5 · 7²

Field	Data	Notes
Atkin-Lehner	2+ 5- 7-	Signs for the Atkin-Lehner involutions
Class	7840h	Isogeny class
Conductor	7840	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	9223681600 = 26 · 52 · 78	Discriminant
Eigenvalues	2+  0 5- 7-  4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-637,-4116]	[a1,a2,a3,a4,a6]
Generators	[875:25872:1]	Generators of the group modulo torsion
j	3796416/1225	j-invariant
L	4.3832359534691	L(r)(E,1)/r!
Ω	0.97464431106994	Real period
R	4.4972672632309	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	7840w1 15680e2 70560dn1 39200bq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7840h1

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	-	-	4	-2	-6	4	-8	6	0	10	-10	12	0	-6	-12	-2	4	-12	10	-4	0	-18	10

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Quadratic twists for elliptic curve 7840h1

-4	8	-3	5	-7
7840w1	15680e2	70560dn1	39200bq1	1120c1

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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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