Cremona's table of elliptic curves

6468 = 2² · 3 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	6468c	Isogeny class
Conductor	6468	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1008	Modular degree for the optimal curve
Δ	-4553472 = -1 · 28 · 3 · 72 · 112	Discriminant
Eigenvalues	2- 3+  0 7- 11+ -3  2  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-93,393]	[a1,a2,a3,a4,a6]
Generators	[-1:22:1]	Generators of the group modulo torsion
j	-7168000/363	j-invariant
L	3.3422688560285	L(r)(E,1)/r!
Ω	2.4196933661969	Real period
R	0.23021297537944	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	25872cu1 103488dq1 19404x1 6468k1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6468c1

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	-	+	-3	2	3	-4	6	5	-5	4	5	6	-10	-12	2	-7	-8	9	11	-4	18	-18

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Quadratic twists for elliptic curve 6468c1

-4	8	-3	-7	-11
25872cu1	103488dq1	19404x1	6468k1	71148o1

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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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