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	2784c	Isogeny class
Conductor	2784	Conductor
∏ cp	24	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]
j	31196377792/613089	j-invariant
L	3.0686230405844	L(r)(E,1)/r!
Ω	2.0457486937229	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2784a1 5568y2 8352j1 69600ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2784c1

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 2784c1

-4	8	-3	5	29
2784a1	5568y2	8352j1	69600ba1	80736h1

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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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