Cremona's table of elliptic curves

6512 = 2⁴ · 11 · 37

Field	Data	Notes
Atkin-Lehner	2- 11+ 37-	Signs for the Atkin-Lehner involutions
Class	6512c	Isogeny class
Conductor	6512	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-1613725696 = -1 · 215 · 113 · 37	Discriminant
Eigenvalues	2-  2 -3 -2 11+  2  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,88,-1936]	[a1,a2,a3,a4,a6]
Generators	[34:198:1]	Generators of the group modulo torsion
j	18191447/393976	j-invariant
L	4.4368511515781	L(r)(E,1)/r!
Ω	0.72831505449648	Real period
R	3.0459696831651	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	814a1 26048j1 58608br1 71632s1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6512c1

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	-3	-2	+	2	3	-2	6	6	10	-	-12	-8	-3	-12	12	8	10	3	-10	-11	-3	-12	-16

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Quadratic twists for elliptic curve 6512c1

-4	8	-3	-11
814a1	26048j1	58608br1	71632s1

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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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