Cremona's table of elliptic curves

1804 = 2² · 11 · 41

Field	Data	Notes
Atkin-Lehner	2- 11- 41+	Signs for the Atkin-Lehner involutions
Class	1804a	Isogeny class
Conductor	1804	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	252	Modular degree for the optimal curve
Δ	-873136 = -1 · 24 · 113 · 41	Discriminant
Eigenvalues	2- -2 -3 -1 11-  2  3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,3,-44]	[a1,a2,a3,a4,a6]
Generators	[3:1:1]	Generators of the group modulo torsion
j	131072/54571	j-invariant
L	1.7449763587445	L(r)(E,1)/r!
Ω	1.3158167915287	Real period
R	1.3261544996072	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	7216e1 28864b1 16236b1 45100b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1804a1

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	-3	-1	-	2	3	5	3	3	-7	-7	+	-10	0	6	-15	14	14	-12	2	8	-6	-6	8

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Quadratic twists for elliptic curve 1804a1

-4	8	-3	5	-7	-11	41
7216e1	28864b1	16236b1	45100b1	88396i1	19844d1	73964c1

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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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