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	3744d	Isogeny class
Conductor	3744	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	672523705152 = 26 · 314 · 133	Discriminant
Eigenvalues	2+ 3- -2 -2 -2 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-26121,-1624444]	[a1,a2,a3,a4,a6]
j	42246001231552/14414517	j-invariant
L	0.75108829412181	L(r)(E,1)/r!
Ω	0.37554414706091	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	3744l1 7488ba2 1248f1 93600ee1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3744d1

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 3744d1

-4	8	-3	5	13
3744l1	7488ba2	1248f1	93600ee1	48672br1

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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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