Cremona's table of elliptic curves

4160 = 2⁶ · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 5- 13-	Signs for the Atkin-Lehner involutions
Class	4160r	Isogeny class
Conductor	4160	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-270400 = -1 · 26 · 52 · 132	Discriminant
Eigenvalues	2-  2 5- -4  6 13- -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-20,50]	[a1,a2,a3,a4,a6]
j	-14526784/4225	j-invariant
L	2.9356519588684	L(r)(E,1)/r!
Ω	2.9356519588684	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	4160t1 2080d2 37440et1 20800cq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4160r1

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

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Quadratic twists for elliptic curve 4160r1

-4	8	-3	5	13
4160t1	2080d2	37440et1	20800cq1	54080ch1

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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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