Cremona's table of elliptic curves

2204 = 2² · 19 · 29

Field	Data	Notes
Atkin-Lehner	2- 19+ 29-	Signs for the Atkin-Lehner involutions
Class	2204b	Isogeny class
Conductor	2204	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	13440	Modular degree for the optimal curve
Δ	-2433198552642304 = -1 · 28 · 19 · 298	Discriminant
Eigenvalues	2-  2 -1 -3 -3  4  5 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-133301,18926849]	[a1,a2,a3,a4,a6]
Generators	[4800:24389:27]	Generators of the group modulo torsion
j	-1023262896933044224/9504681846259	j-invariant
L	3.6952374762068	L(r)(E,1)/r!
Ω	0.46077453921701	Real period
R	1.0024527078053	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	8816l1 35264m1 19836d1 55100e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2204b1

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	-1	-3	-3	4	5	+	-8	-	-4	2	10	-7	-9	-4	-10	-5	-4	-6	1	-8	4	-4	-8

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Quadratic twists for elliptic curve 2204b1

-4	8	-3	5	-7	-19	29
8816l1	35264m1	19836d1	55100e1	107996h1	41876a1	63916e1

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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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