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	3744c	Isogeny class
Conductor	3744	Conductor
∏ cp	16	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]
j	778688/1521	j-invariant
L	2.8745108264748	L(r)(E,1)/r!
Ω	0.71862770661871	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3744k2 7488bc1 1248i2 93600ej2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3744c2

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 3744c2

-4	8	-3	5	13
3744k2	7488bc1	1248i2	93600ej2	48672bv2

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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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