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	3744f	Isogeny class
Conductor	3744	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1513893888 = 212 · 37 · 132	Discriminant
Eigenvalues	2+ 3-  0 -2  0 13- -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-300,704]	[a1,a2,a3,a4,a6]
Generators	[-10:52:1]	Generators of the group modulo torsion
j	1000000/507	j-invariant
L	3.409477155763	L(r)(E,1)/r!
Ω	1.3329593406492	Real period
R	0.63945633069768	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	3744e2 7488bo1 1248g2 93600dj2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3744f2

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
+	-	0	-2	0	-	-2	2	8	-6	-2	-6	0	-4	8	6	4	2	-2	4	-2	-12	-12	-12	-18

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Quadratic twists for elliptic curve 3744f2

-4	8	-3	5	13
3744e2	7488bo1	1248g2	93600dj2	48672bm2

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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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