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	13680t	Isogeny class
Conductor	13680	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	1884413258496000 = 211 · 318 · 53 · 19	Discriminant
Eigenvalues	2+ 3- 5-  0 -4 -2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-914187,-336428134]	[a1,a2,a3,a4,a6]
Generators	[-553:70:1]	Generators of the group modulo torsion
j	56594125707224978/1262172375	j-invariant
L	4.8691691849749	L(r)(E,1)/r!
Ω	0.15439789517327	Real period
R	2.6280416471517	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	6840u4 54720dt4 4560a4 68400bf4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13680t3

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

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Quadratic twists for elliptic curve 13680t3

-4	8	-3	5
6840u4	54720dt4	4560a4	68400bf4

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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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