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	7865b	Isogeny class
Conductor	7865	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-7484845225 = -1 · 52 · 116 · 132	Discriminant
Eigenvalues	1 -2 5+  4 11- 13- -2  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,481,-849]	[a1,a2,a3,a4,a6]
Generators	[3:23:1]	Generators of the group modulo torsion
j	6967871/4225	j-invariant
L	3.5637126765735	L(r)(E,1)/r!
Ω	0.76660117009832	Real period
R	2.3243590119465	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	125840by2 70785bf2 39325d2 65a2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 7865b2

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	+	4	-	-	-2	6	-6	-2	-10	-2	6	-10	4	2	6	-2	-4	6	6	12	16	2	-2

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Quadratic twists for elliptic curve 7865b2

-4	-3	5	-11	13
125840by2	70785bf2	39325d2	65a2	102245l2

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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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