Cremona's table of elliptic curves

1850 = 2 · 5² · 37

Field	Data	Notes
Atkin-Lehner	2+ 5+ 37+	Signs for the Atkin-Lehner involutions
Class	1850a	Isogeny class
Conductor	1850	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	296000000000 = 212 · 59 · 37	Discriminant
Eigenvalues	2+  2 5+ -2  0 -2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1875,-17875]	[a1,a2,a3,a4,a6]
Generators	[-19:116:1]	Generators of the group modulo torsion
j	46694890801/18944000	j-invariant
L	2.8259621973929	L(r)(E,1)/r!
Ω	0.75158788142571	Real period
R	3.7599890408453	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	14800q1 59200bf1 16650bz1 370d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1850a1

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	+	-2	0	-2	-6	2	0	6	-10	+	-6	4	6	-6	-6	-10	-2	0	-2	-10	6	-6	-2

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Quadratic twists for elliptic curve 1850a1

-4	8	-3	5	-7	37
14800q1	59200bf1	16650bz1	370d1	90650j1	68450y1

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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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