Cremona's table of elliptic curves

185 = 5 · 37

Field	Data	Notes
Atkin-Lehner	5+ 37+	Signs for the Atkin-Lehner involutions
Class	185a	Isogeny class
Conductor	185	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	23125 = 54 · 37	Discriminant
Eigenvalues	-2  1 5+ -5  3 -2 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-156,700]	[a1,a2,a3,a4,a6]
Generators	[4:12:1]	Generators of the group modulo torsion
j	422550360064/23125	j-invariant
L	0.81962981763016	L(r)(E,1)/r!
Ω	3.593080397514	Real period
R	0.11405670440846	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	2960f1 11840r1 1665g1 925d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 185a1

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
-2	1	+	-5	3	-2	-4	-4	-2	2	0	+	7	-10	11	-3	0	-4	16	-15	11	-12	-3	-4	8

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Quadratic twists for elliptic curve 185a1

-4	8	-3	5	-7	-11	13	17	-19	-23	37
2960f1	11840r1	1665g1	925d1	9065e1	22385d1	31265f1	53465g1	66785e1	97865d1	6845d1

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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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