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	8	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	-292032 = -1 · 26 · 33 · 132	Discriminant
Eigenvalues	2- 3+  2  0 -2 13-  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-9,28]	[a1,a2,a3,a4,a6]
Generators	[-1:6:1]	Generators of the group modulo torsion
j	-46656/169	j-invariant
L	3.9421321366483	L(r)(E,1)/r!
Ω	2.6920092925214	Real period
R	0.73219140580232	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	3744a1 7488c2 3744b1 93600b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3744i1

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 3744i1

-4	8	-3	5	13
3744a1	7488c2	3744b1	93600b1	48672d1

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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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