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	256	Product of Tamagawa factors cp
Δ	9.8585386746643E+23	Discriminant
Eigenvalues	2- 3- 5- -4  0  2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-33661947,58041215786]	[a1,a2,a3,a4,a6]
Generators	[-3113:364230:1]	Generators of the group modulo torsion
j	1412712966892699019449/330160465517040000	j-invariant
L	4.4952347675749	L(r)(E,1)/r!
Ω	0.082710226753986	Real period
R	3.3968250843889	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1710s3 54720dr3 4560q3 68400fq3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13680bx4

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 13680bx4

-4	8	-3	5
1710s3	54720dr3	4560q3	68400fq3

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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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