Cremona's table of elliptic curves

13680 = 2⁴ · 3² · 5 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 19-	Signs for the Atkin-Lehner involutions
Class	13680c	Isogeny class
Conductor	13680	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	13132800 = 210 · 33 · 52 · 19	Discriminant
Eigenvalues	2+ 3+ 5+ -4 -2 -4 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-483,4082]	[a1,a2,a3,a4,a6]
Generators	[-14:90:1] [1:60:1]	Generators of the group modulo torsion
j	450714348/475	j-invariant
L	5.8054924889773	L(r)(E,1)/r!
Ω	2.2307436513086	Real period
R	0.65062299802701	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6840k1 54720de1 13680f1 68400p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13680c1

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
+	+	+	-4	-2	-4	-4	-	0	-2	-2	-8	-6	-12	-12	2	-12	14	-16	8	6	-2	10	-14	-6

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Quadratic twists for elliptic curve 13680c1

-4	8	-3	5
6840k1	54720de1	13680f1	68400p1

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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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