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	4160i	Isogeny class
Conductor	4160	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	-6922240000000000 = -1 · 222 · 510 · 132	Discriminant
Eigenvalues	2+ -2 5- -4  2 13-  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-48705,-5773025]	[a1,a2,a3,a4,a6]
Generators	[315:3200:1]	Generators of the group modulo torsion
j	-48743122863889/26406250000	j-invariant
L	2.4066951498031	L(r)(E,1)/r!
Ω	0.15672092876756	Real period
R	0.76782825648405	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	4160q2 130c2 37440bx2 20800n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4160i2

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

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Quadratic twists for elliptic curve 4160i2

-4	8	-3	5	13
4160q2	130c2	37440bx2	20800n2	54080u2

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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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