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	3784f	Isogeny class
Conductor	3784	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-630020864 = -1 · 28 · 113 · 432	Discriminant
Eigenvalues	2+ -1 -1 -4 11- -6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,199,-611]	[a1,a2,a3,a4,a6]
Generators	[5:22:1] [17:86:1]	Generators of the group modulo torsion
j	3387339776/2461019	j-invariant
L	3.4102465283839	L(r)(E,1)/r!
Ω	0.91149962574248	Real period
R	0.15588992176888	Regulator
r	2	Rank of the group of rational points
S	0.99999999999976	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7568c1 30272f1 34056r1 94600t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3784f1

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
+	-1	-1	-4	-	-6	-6	-4	-7	-2	1	5	0	+	0	10	-5	4	-13	-15	-4	-8	-18	5	5

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Quadratic twists for elliptic curve 3784f1

-4	8	-3	5	-11
7568c1	30272f1	34056r1	94600t1	41624q1

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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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