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	8	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	39237696 = 26 · 36 · 292	Discriminant
Eigenvalues	2+ 3+  2  0 -4 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-262,-1520]	[a1,a2,a3,a4,a6]
Generators	[1342:49140:1]	Generators of the group modulo torsion
j	31196377792/613089	j-invariant
L	3.0963801081717	L(r)(E,1)/r!
Ω	1.1876945888787	Real period
R	5.2141015664559	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2784c1 5568bf2 8352i1 69600bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2784a1

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 2784a1

-4	8	-3	5	29
2784c1	5568bf2	8352i1	69600bl1	80736m1

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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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