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	6864p	Isogeny class
Conductor	6864	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	31104	Modular degree for the optimal curve
Δ	1647851208548688 = 24 · 318 · 112 · 133	Discriminant
Eigenvalues	2- 3+  0 -2 11- 13-  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-95173,11162788]	[a1,a2,a3,a4,a6]
j	5958673237147648000/102990700534293	j-invariant
L	1.4229490798248	L(r)(E,1)/r!
Ω	0.4743163599416	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1716b1 27456bx1 20592be1 75504bg1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6864p1

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

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Quadratic twists for elliptic curve 6864p1

-4	8	-3	-11	13
1716b1	27456bx1	20592be1	75504bg1	89232x1

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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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