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	6864f	Isogeny class
Conductor	6864	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	18816	Modular degree for the optimal curve
Δ	-51576064809984 = -1 · 210 · 37 · 116 · 13	Discriminant
Eigenvalues	2+ 3+  2  0 11- 13-  8 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,5928,-299520]	[a1,a2,a3,a4,a6]
Generators	[62:550:1]	Generators of the group modulo torsion
j	22494434350748/50367250791	j-invariant
L	4.1422536616086	L(r)(E,1)/r!
Ω	0.32792566336717	Real period
R	2.1052808224257	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	3432h1 27456ca1 20592f1 75504b1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6864f1

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	-	-	8	-2	-6	-6	-6	-8	-6	0	-8	-12	-4	10	8	-12	16	0	4	6	-6

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Quadratic twists for elliptic curve 6864f1

-4	8	-3	-11	13
3432h1	27456ca1	20592f1	75504b1	89232c1

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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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