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	6864s	Isogeny class
Conductor	6864	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	-215595933696 = -1 · 213 · 32 · 113 · 133	Discriminant
Eigenvalues	2- 3+ -3 -5 11- 13-  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9872,381504]	[a1,a2,a3,a4,a6]
Generators	[-746569040:6168700824:8365427] [482:-10362:1]	Generators of the group modulo torsion
j	-25979045828113/52635726	j-invariant
L	3.8357468667001	L(r)(E,1)/r!
Ω	0.9992976881792	Real period
R	0.053311703477044	Regulator
r	2	Rank of the group of rational points
S	0.99999999999994	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	858j2 27456cb2 20592bj2 75504bq2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6864s2

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	-5	-	-	0	-2	-3	-3	-8	-10	-3	-5	-12	-6	9	-13	-5	-6	-7	10	-6	0	-10

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Quadratic twists for elliptic curve 6864s2

-4	8	-3	-11	13
858j2	27456cb2	20592bj2	75504bq2	89232be2

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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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