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	13680bx	Isogeny class
Conductor	13680	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	430080	Modular degree for the optimal curve
Δ	-3.5156921131777E+20	Discriminant
Eigenvalues	2- 3- 5- -4  0  2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,529413,-889851094]	[a1,a2,a3,a4,a6]
Generators	[74797080:5536054529:13824]	Generators of the group modulo torsion
j	5495662324535111/117739817533440	j-invariant
L	4.4952347675749	L(r)(E,1)/r!
Ω	0.082710226753986	Real period
R	13.587300337556	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	1710s1 54720dr1 4560q1 68400fq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13680bx1

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

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Quadratic twists for elliptic curve 13680bx1

-4	8	-3	5
1710s1	54720dr1	4560q1	68400fq1

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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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