Cremona's table of elliptic curves

6816 = 2⁵ · 3 · 71

Field	Data	Notes
Atkin-Lehner	2+ 3+ 71-	Signs for the Atkin-Lehner involutions
Class	6816b	Isogeny class
Conductor	6816	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	-21733811136 = -1 · 26 · 314 · 71	Discriminant
Eigenvalues	2+ 3+ -2 -2  0 -2 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-634,-9176]	[a1,a2,a3,a4,a6]
j	-441058644928/339590799	j-invariant
L	0.46034066758166	L(r)(E,1)/r!
Ω	0.46034066758166	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	6816f1 13632j2 20448i1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 6816b1

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	-2	0	-2	-4	0	0	10	2	-6	-4	-4	-12	-12	-4	2	2	-	-10	16	-4	-18	-10

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Quadratic twists for elliptic curve 6816b1

-4	8	-3
6816f1	13632j2	20448i1

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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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