Cremona's table of elliptic curves

1845 = 3² · 5 · 41

Field	Data	Notes
Atkin-Lehner	3- 5- 41+	Signs for the Atkin-Lehner involutions
Class	1845f	Isogeny class
Conductor	1845	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	747225 = 36 · 52 · 41	Discriminant
Eigenvalues	1 3- 5-  2 -6  2 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-189,1048]	[a1,a2,a3,a4,a6]
Generators	[12:14:1]	Generators of the group modulo torsion
j	1027243729/1025	j-invariant
L	3.7319199196217	L(r)(E,1)/r!
Ω	2.8309677097514	Real period
R	1.3182488471228	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	29520bz1 118080x1 205b1 9225q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1845f1

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	-6	2	-2	-6	4	-10	0	-6	+	-4	2	14	-12	-10	-2	2	6	-2	0	-10	10

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Quadratic twists for elliptic curve 1845f1

-4	8	-3	5	-7	41
29520bz1	118080x1	205b1	9225q1	90405y1	75645q1

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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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