Cremona's table of elliptic curves

2784 = 2⁵ · 3 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3+ 29+	Signs for the Atkin-Lehner involutions
Class	2784a	Isogeny class
Conductor	2784	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-9777452544 = -1 · 29 · 33 · 294	Discriminant
Eigenvalues	2+ 3+  2  0 -4 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,8,-4760]	[a1,a2,a3,a4,a6]
Generators	[167745:6142682:125]	Generators of the group modulo torsion
j	97336/19096587	j-invariant
L	3.0963801081717	L(r)(E,1)/r!
Ω	0.59384729443933	Real period
R	10.428203132912	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	2784c4 5568bf4 8352i4 69600bl2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2784a4

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	-4	-2	6	-4	0	+	0	-6	-2	4	-12	-6	4	10	-8	0	2	8	-12	6	2

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Quadratic twists for elliptic curve 2784a4

-4	8	-3	5	29
2784c4	5568bf4	8352i4	69600bl2	80736m2

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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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