Cremona's table of elliptic curves

185 = 5 · 37

Field	Data	Notes
Atkin-Lehner	5- 37-	Signs for the Atkin-Lehner involutions
Class	185b	Isogeny class
Conductor	185	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	925 = 52 · 37	Discriminant
Eigenvalues	0 -1 5- -3 -5  4 -4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-5,6]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	16777216/925	j-invariant
L	1.0803747090133	L(r)(E,1)/r!
Ω	4.8983715400719	Real period
R	0.11027896722157	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	2960m1 11840a1 1665d1 925a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 185b1

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	-1	-	-3	-5	4	-4	-8	4	4	2	-	-5	-6	9	3	-8	-10	-4	5	-15	-14	11	-2	10

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Quadratic twists for elliptic curve 185b1

-4	8	-3	5	-7	-11	13	17	-19	-23	37
2960m1	11840a1	1665d1	925a1	9065b1	22385m1	31265a1	53465b1	66785f1	97865a1	6845a1

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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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