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	7840n	Isogeny class
Conductor	7840	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-12047257600 = -1 · 212 · 52 · 76	Discriminant
Eigenvalues	2+  2 5- 7- -4  6 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-65,-5263]	[a1,a2,a3,a4,a6]
Generators	[37:204:1]	Generators of the group modulo torsion
j	-64/25	j-invariant
L	6.0839200572723	L(r)(E,1)/r!
Ω	0.56912991838073	Real period
R	2.6724653988416	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	7840y2 15680w1 70560dg2 39200cg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7840n2

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

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Quadratic twists for elliptic curve 7840n2

-4	8	-3	5	-7
7840y2	15680w1	70560dg2	39200cg2	160a2

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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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