Cremona's table of elliptic curves

2812 = 2² · 19 · 37

Field	Data	Notes
Atkin-Lehner	2- 19- 37+	Signs for the Atkin-Lehner involutions
Class	2812b	Isogeny class
Conductor	2812	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	3419392 = 28 · 192 · 37	Discriminant
Eigenvalues	2-  1 -2  5 -3 -2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-149,647]	[a1,a2,a3,a4,a6]
Generators	[2:19:1]	Generators of the group modulo torsion
j	1438646272/13357	j-invariant
L	3.7109626374726	L(r)(E,1)/r!
Ω	2.5184933705435	Real period
R	0.73674258603899	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	11248e1 44992l1 25308f1 70300c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2812b1

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	-2	5	-3	-2	2	-	-8	-10	4	+	-11	12	9	-9	-10	-12	-4	9	3	4	3	-6	-18

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Quadratic twists for elliptic curve 2812b1

-4	8	-3	5	-19	37
11248e1	44992l1	25308f1	70300c1	53428f1	104044a1

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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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