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	13680bl	Isogeny class
Conductor	13680	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	20480	Modular degree for the optimal curve
Δ	-1309697372160 = -1 · 212 · 311 · 5 · 192	Discriminant
Eigenvalues	2- 3- 5-  2 -6  0  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2733,-2734]	[a1,a2,a3,a4,a6]
j	756058031/438615	j-invariant
L	2.0376398802495	L(r)(E,1)/r!
Ω	0.50940997006236	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	855c1 54720ea1 4560k1 68400ep1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13680bl1

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

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Quadratic twists for elliptic curve 13680bl1

-4	8	-3	5
855c1	54720ea1	4560k1	68400ep1

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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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