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	6864ba	Isogeny class
Conductor	6864	Conductor
∏ cp	120	Product of Tamagawa factors cp
deg	63360	Modular degree for the optimal curve
Δ	-24976229438324736 = -1 · 223 · 36 · 11 · 135	Discriminant
Eigenvalues	2- 3- -3 -1 11- 13- -8  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9152,-7614156]	[a1,a2,a3,a4,a6]
Generators	[970:29952:1]	Generators of the group modulo torsion
j	-20699471212993/6097712265216	j-invariant
L	3.9365691484494	L(r)(E,1)/r!
Ω	0.16898770628538	Real period
R	0.19412502616223	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	858f1 27456bk1 20592bh1 75504cr1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6864ba1

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
-	-	-3	-1	-	-	-8	6	1	1	0	6	-11	11	12	2	-7	11	-9	2	-11	-6	-14	0	6

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Quadratic twists for elliptic curve 6864ba1

-4	8	-3	-11	13
858f1	27456bk1	20592bh1	75504cr1	89232ce1

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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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