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	6468b	Isogeny class
Conductor	6468	Conductor
∏ cp	45	Product of Tamagawa factors cp
deg	50400	Modular degree for the optimal curve
Δ	-57755584691659008 = -1 · 28 · 35 · 78 · 115	Discriminant
Eigenvalues	2- 3+ -2 7+ 11-  2  3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,85636,-6404712]	[a1,a2,a3,a4,a6]
Generators	[82:1078:1]	Generators of the group modulo torsion
j	47061251888/39135393	j-invariant
L	3.0241847421902	L(r)(E,1)/r!
Ω	0.19477890693901	Real period
R	0.34502763383432	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	25872ce1 103488ch1 19404i1 6468r1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6468b1

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	3	-1	-7	-1	8	-11	6	-9	1	-2	9	4	-2	15	-6	12	12	0	-5

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Quadratic twists for elliptic curve 6468b1

-4	8	-3	-7	-11
25872ce1	103488ch1	19404i1	6468r1	71148h1

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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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