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	1845d	Isogeny class
Conductor	1845	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	747225 = 36 · 52 · 41	Discriminant
Eigenvalues	-1 3- 5+  2  0 -4 -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-23,6]	[a1,a2,a3,a4,a6]
Generators	[-4:6:1]	Generators of the group modulo torsion
j	1771561/1025	j-invariant
L	1.8832547411681	L(r)(E,1)/r!
Ω	2.4074027760147	Real period
R	0.78227655128222	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	29520bq1 118080cq1 205c1 9225x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1845d1

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	0	-4	-4	0	8	-2	0	-6	-	8	-2	-8	12	2	10	-8	-6	-8	-12	-14	-8

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Quadratic twists for elliptic curve 1845d1

-4	8	-3	5	-7	41
29520bq1	118080cq1	205c1	9225x1	90405bm1	75645i1

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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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