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
Δ	33171021564453125 = 59 · 198	Discriminant
Eigenvalues	0 -2 5+ -4  3  2  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-105171,-9810339]	[a1,a2,a3,a4,a6]
Generators	[-241:1263:1]	Generators of the group modulo torsion
j	7575076864/1953125	j-invariant
L	1.4603328767337	L(r)(E,1)/r!
Ω	0.27016308125806	Real period
R	1.8017918040879	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	28880q2 115520u2 16245e2 9025b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1805a2

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 1805a2

-4	8	-3	5	-7	-19
28880q2	115520u2	16245e2	9025b2	88445bh2	1805b2

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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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