Cremona's table of elliptic curves

1805 = 5 · 19²

Field	Data	Notes
Atkin-Lehner	5+ 19+	Signs for the Atkin-Lehner involutions
Class	1805a	Isogeny class
Conductor	1805	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	4788	Modular degree for the optimal curve
Δ	2122945380125 = 53 · 198	Discriminant
Eigenvalues	0 -2 5+ -4  3  2  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-36581,2679900]	[a1,a2,a3,a4,a6]
Generators	[-78:2250:1]	Generators of the group modulo torsion
j	318767104/125	j-invariant
L	1.4603328767337	L(r)(E,1)/r!
Ω	0.81048924377418	Real period
R	5.4053754122638	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	28880q1 115520u1 16245e1 9025b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1805a1

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
0	-2	+	-4	3	2	6	+	0	-3	-7	8	-6	-4	6	-6	-15	5	2	-3	8	5	12	-15	8

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Quadratic twists for elliptic curve 1805a1

-4	8	-3	5	-7	-19
28880q1	115520u1	16245e1	9025b1	88445bh1	1805b1

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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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