Cremona's table of elliptic curves

13776 = 2⁴ · 3 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 41+	Signs for the Atkin-Lehner involutions
Class	13776h	Isogeny class
Conductor	13776	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	13440	Modular degree for the optimal curve
Δ	-255950585856 = -1 · 219 · 35 · 72 · 41	Discriminant
Eigenvalues	2- 3+ -3 7-  0 -5 -1  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-512,-24576]	[a1,a2,a3,a4,a6]
Generators	[64:448:1]	Generators of the group modulo torsion
j	-3630961153/62487936	j-invariant
L	2.9132514711439	L(r)(E,1)/r!
Ω	0.42289496049728	Real period
R	0.86110374421293	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	1722n1 55104de1 41328ck1 96432db1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13776h1

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
-	+	-3	-	0	-5	-1	1	2	0	9	-8	+	-6	8	0	-3	0	5	-3	3	4	5	3	-8

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Quadratic twists for elliptic curve 13776h1

-4	8	-3	-7
1722n1	55104de1	41328ck1	96432db1

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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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