Cremona's table of elliptic curves

6864 = 2⁴ · 3 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 11- 13-	Signs for the Atkin-Lehner involutions
Class	6864r	Isogeny class
Conductor	6864	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	5271552 = 212 · 32 · 11 · 13	Discriminant
Eigenvalues	2- 3+ -2  0 11- 13- -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-109824,-13972032]	[a1,a2,a3,a4,a6]
j	35765103905346817/1287	j-invariant
L	1.0490227386953	L(r)(E,1)/r!
Ω	0.26225568467382	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	429b4 27456bz4 20592bg4 75504bj4	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6864r3

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	0	-	-	-6	4	8	-10	0	6	10	-4	-8	-10	12	14	12	0	-6	-8	-12	2	-14

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Quadratic twists for elliptic curve 6864r3

-4	8	-3	-11	13
429b4	27456bz4	20592bg4	75504bj4	89232bd4

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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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