Cremona's table of elliptic curves

3741 = 3 · 29 · 43

Field	Data	Notes
Atkin-Lehner	3+ 29+ 43+	Signs for the Atkin-Lehner involutions
Class	3741a	Isogeny class
Conductor	3741	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2280	Modular degree for the optimal curve
Δ	2645938221 = 3 · 295 · 43	Discriminant
Eigenvalues	0 3+  3 -2 -5 -2  7 -3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-649,-5652]	[a1,a2,a3,a4,a6]
Generators	[-16:19:1]	Generators of the group modulo torsion
j	30277973573632/2645938221	j-invariant
L	2.7238465051758	L(r)(E,1)/r!
Ω	0.95103688559142	Real period
R	2.8640808221459	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	59856p1 11223d1 93525n1 108489k1	Quadratic twists by: -4 -3 5 29

Hecke Eigenvalues for elliptic curve 3741a1

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	+	3	-2	-5	-2	7	-3	4	+	10	-2	3	+	-8	-2	-8	7	5	-9	-13	-6	0	0	16

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Quadratic twists for elliptic curve 3741a1

-4	-3	5	29
59856p1	11223d1	93525n1	108489k1

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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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