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	13680bd	Isogeny class
Conductor	13680	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	184320	Modular degree for the optimal curve
Δ	-121036992345538560 = -1 · 220 · 311 · 5 · 194	Discriminant
Eigenvalues	2- 3- 5+ -4  0 -6 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-273603,57571522]	[a1,a2,a3,a4,a6]
Generators	[-223:10368:1]	Generators of the group modulo torsion
j	-758575480593601/40535043840	j-invariant
L	3.3167389435412	L(r)(E,1)/r!
Ω	0.32707772641431	Real period
R	1.2675652741254	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	1710g1 54720fc1 4560bc1 68400eq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13680bd1

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

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Quadratic twists for elliptic curve 13680bd1

-4	8	-3	5
1710g1	54720fc1	4560bc1	68400eq1

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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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