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	3744j	Isogeny class
Conductor	3744	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-212891328 = -1 · 26 · 39 · 132	Discriminant
Eigenvalues	2- 3+ -2  0 -2 13-  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-81,756]	[a1,a2,a3,a4,a6]
Generators	[1:26:1]	Generators of the group modulo torsion
j	-46656/169	j-invariant
L	3.1393857170616	L(r)(E,1)/r!
Ω	1.5542322896982	Real period
R	1.0099473990697	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	3744b1 7488a2 3744a1 93600a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3744j1

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	0	-2	-	0	4	-4	8	8	2	-6	-4	-6	4	-6	2	4	-6	-2	-16	-2	-10	-2

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Quadratic twists for elliptic curve 3744j1

-4	8	-3	5	13
3744b1	7488a2	3744a1	93600a1	48672a1

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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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