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	7840b	Isogeny class
Conductor	7840	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-2951578112000 = -1 · 212 · 53 · 78	Discriminant
Eigenvalues	2+ -1 5+ 7+ -2  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3201,109201]	[a1,a2,a3,a4,a6]
Generators	[33:196:1]	Generators of the group modulo torsion
j	-153664/125	j-invariant
L	2.9868402294458	L(r)(E,1)/r!
Ω	0.73574123597651	Real period
R	0.33830284382995	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	7840a1 15680cz1 70560dr1 39200bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7840b1

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	+	+	-2	2	-2	0	1	-1	-2	4	5	11	8	-8	-4	-5	-1	-12	6	4	13	-3	-2

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Quadratic twists for elliptic curve 7840b1

-4	8	-3	5	-7
7840a1	15680cz1	70560dr1	39200bl1	7840j1

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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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