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	3744k	Isogeny class
Conductor	3744	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-4541681664 = -1 · 212 · 38 · 132	Discriminant
Eigenvalues	2- 3-  2 -2 -6 13+  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,276,2720]	[a1,a2,a3,a4,a6]
Generators	[5:65:1]	Generators of the group modulo torsion
j	778688/1521	j-invariant
L	3.6622192522209	L(r)(E,1)/r!
Ω	0.94970504555875	Real period
R	1.9280824448322	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	3744c2 7488bd1 1248a2 93600bq2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3744k2

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

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Quadratic twists for elliptic curve 3744k2

-4	8	-3	5	13
3744c2	7488bd1	1248a2	93600bq2	48672t2

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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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