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	3744i	Isogeny class
Conductor	3744	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1437696 = 212 · 33 · 13	Discriminant
Eigenvalues	2- 3+  2  0 -2 13-  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-204,1120]	[a1,a2,a3,a4,a6]
Generators	[5:15:1]	Generators of the group modulo torsion
j	8489664/13	j-invariant
L	3.9421321366483	L(r)(E,1)/r!
Ω	2.6920092925214	Real period
R	1.4643828116046	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	3744a2 7488c1 3744b2 93600b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3744i2

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 3744i2

-4	8	-3	5	13
3744a2	7488c1	3744b2	93600b2	48672d2

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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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