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	7840r	Isogeny class
Conductor	7840	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	-10541350400000 = -1 · 212 · 55 · 77	Discriminant
Eigenvalues	2- -1 5+ 7- -3  7  5 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1699,153301]	[a1,a2,a3,a4,a6]
Generators	[-37:196:1]	Generators of the group modulo torsion
j	1124864/21875	j-invariant
L	3.137026319581	L(r)(E,1)/r!
Ω	0.53883698051329	Real period
R	1.4554616855513	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	7840c1 15680bn1 70560bo1 39200k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7840r1

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	+	-	-3	7	5	-4	-4	-5	2	0	-6	8	-9	0	-12	6	16	-4	14	-9	8	6	-3

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Quadratic twists for elliptic curve 7840r1

-4	8	-3	5	-7
7840c1	15680bn1	70560bo1	39200k1	1120m1

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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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