Cremona's table of elliptic curves

13376 = 2⁶ · 11 · 19

Field	Data	Notes
Atkin-Lehner	2+ 11- 19-	Signs for the Atkin-Lehner involutions
Class	13376k	Isogeny class
Conductor	13376	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	10240	Modular degree for the optimal curve
Δ	-23486971904 = -1 · 214 · 11 · 194	Discriminant
Eigenvalues	2+ -1  3  2 11- -4 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2469,-46979]	[a1,a2,a3,a4,a6]
Generators	[300:5111:1]	Generators of the group modulo torsion
j	-101634915328/1433531	j-invariant
L	4.8531760357711	L(r)(E,1)/r!
Ω	0.33834544296502	Real period
R	3.5859623180094	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	13376m1 1672b1 120384be1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 13376k1

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
+	-1	3	2	-	-4	-2	-	-7	-4	-3	5	4	2	0	14	5	8	-7	-9	8	6	-2	-13	-11

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Quadratic twists for elliptic curve 13376k1

-4	8	-3
13376m1	1672b1	120384be1

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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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