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	7840p	Isogeny class
Conductor	7840	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	8681255332467200 = 29 · 52 · 714	Discriminant
Eigenvalues	2-  0 5+ 7-  0  2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-52283,-1037918]	[a1,a2,a3,a4,a6]
Generators	[-8316:120785:64]	Generators of the group modulo torsion
j	262389836808/144120025	j-invariant
L	3.7908623266969	L(r)(E,1)/r!
Ω	0.33754879163193	Real period
R	5.6152805471018	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	7840q2 15680dj4 70560bg3 39200d3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7840p3

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	+	-	0	2	-2	8	-8	6	0	-2	6	-8	-8	-2	8	2	-8	0	-10	16	16	-10	14

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Quadratic twists for elliptic curve 7840p3

-4	8	-3	5	-7
7840q2	15680dj4	70560bg3	39200d3	1120l2

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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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