Cremona's table of elliptic curves

3784 = 2³ · 11 · 43

Field	Data	Notes
Atkin-Lehner	2- 11- 43+	Signs for the Atkin-Lehner involutions
Class	3784g	Isogeny class
Conductor	3784	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	224	Modular degree for the optimal curve
Δ	7568 = 24 · 11 · 43	Discriminant
Eigenvalues	2- -2  0 -3 11-  2  4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-8,-11]	[a1,a2,a3,a4,a6]
Generators	[-2:1:1]	Generators of the group modulo torsion
j	4000000/473	j-invariant
L	2.2670840686645	L(r)(E,1)/r!
Ω	2.8316322352859	Real period
R	0.40031400271787	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	7568d1 30272g1 34056c1 94600f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3784g1

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	-3	-	2	4	-5	1	9	-9	2	6	+	9	-9	15	5	-3	8	-6	-8	-10	10	5

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Quadratic twists for elliptic curve 3784g1

-4	8	-3	5	-11
7568d1	30272g1	34056c1	94600f1	41624g1

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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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