Cremona's table of elliptic curves

7865 = 5 · 11² · 13

Field	Data	Notes
Atkin-Lehner	5- 11- 13+	Signs for the Atkin-Lehner involutions
Class	7865d	Isogeny class
Conductor	7865	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-31666652875 = -1 · 53 · 117 · 13	Discriminant
Eigenvalues	0 -2 5- -2 11- 13+  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-645,-10851]	[a1,a2,a3,a4,a6]
Generators	[51:302:1]	Generators of the group modulo torsion
j	-16777216/17875	j-invariant
L	2.035379778133	L(r)(E,1)/r!
Ω	0.45442916205641	Real period
R	0.74649690501168	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	125840cj1 70785i1 39325j1 715a1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 7865d1

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	-2	-	-2	-	+	3	-5	-6	6	-10	-1	9	7	9	-12	0	4	5	0	-2	10	-6	0	17

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Quadratic twists for elliptic curve 7865d1

-4	-3	5	-11	13
125840cj1	70785i1	39325j1	715a1	102245a1

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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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