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	13776c	Isogeny class
Conductor	13776	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	-23804928 = -1 · 210 · 34 · 7 · 41	Discriminant
Eigenvalues	2+ 3+  0 7- -2  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,72,0]	[a1,a2,a3,a4,a6]
Generators	[8:32:1]	Generators of the group modulo torsion
j	39753500/23247	j-invariant
L	4.0644134567888	L(r)(E,1)/r!
Ω	1.2907013680426	Real period
R	1.5744980045046	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6888a1 55104df1 41328l1 96432k1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13776c1

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

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Quadratic twists for elliptic curve 13776c1

-4	8	-3	-7
6888a1	55104df1	41328l1	96432k1

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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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