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	3744b	Isogeny class
Conductor	3744	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1048080384 = 212 · 39 · 13	Discriminant
Eigenvalues	2+ 3+ -2  0  2 13-  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1836,-30240]	[a1,a2,a3,a4,a6]
j	8489664/13	j-invariant
L	1.4588186985337	L(r)(E,1)/r!
Ω	0.72940934926685	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	3744j2 7488b1 3744i2 93600cr2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3744b2

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 3744b2

-4	8	-3	5	13
3744j2	7488b1	3744i2	93600cr2	48672bb2

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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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