Cremona's table of elliptic curves

3540 = 2² · 3 · 5 · 59

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 59+	Signs for the Atkin-Lehner involutions
Class	3540f	Isogeny class
Conductor	3540	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	177447456000 = 28 · 33 · 53 · 593	Discriminant
Eigenvalues	2- 3- 5+ -4  3 -1  3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9141,-338841]	[a1,a2,a3,a4,a6]
Generators	[-54:15:1]	Generators of the group modulo torsion
j	329998817296384/693154125	j-invariant
L	3.6487271607504	L(r)(E,1)/r!
Ω	0.4883171471275	Real period
R	2.4906813001986	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	14160p2 56640r2 10620o2 17700a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3540f2

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	3	-1	3	5	-6	-6	-4	-1	-6	-1	0	-3	+	2	-7	12	-1	5	-6	-15	2

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Quadratic twists for elliptic curve 3540f2

-4	8	-3	5
14160p2	56640r2	10620o2	17700a2

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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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