Cremona's table of elliptic curves

3744 = 2⁵ · 3² · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 13+	Signs for the Atkin-Lehner involutions
Class	3744l	Isogeny class
Conductor	3744	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1167434730049536 = -1 · 212 · 310 · 136	Discriminant
Eigenvalues	2- 3- -2  2  2 13+ -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-22476,2093920]	[a1,a2,a3,a4,a6]
Generators	[-148:1476:1]	Generators of the group modulo torsion
j	-420526439488/390971529	j-invariant
L	3.3702649038632	L(r)(E,1)/r!
Ω	0.44500132597093	Real period
R	3.7868032151475	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	3744d2 7488z1 1248c2 93600bs2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3744l2

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	2	2	+	-6	2	0	-2	-2	10	-2	-8	-2	2	10	6	-14	-14	-6	4	6	-10	10

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Quadratic twists for elliptic curve 3744l2

-4	8	-3	5	13
3744d2	7488z1	1248c2	93600bs2	48672q2

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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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