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	16	Product of Tamagawa factors cp
Δ	-4008947514062500 = -1 · 22 · 58 · 376	Discriminant
Eigenvalues	2+  2 5+ -2  0 -2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-131375,-18634375]	[a1,a2,a3,a4,a6]
Generators	[1780:72535:1]	Generators of the group modulo torsion
j	-16048965315233521/256572640900	j-invariant
L	2.8259621973929	L(r)(E,1)/r!
Ω	0.12526464690429	Real period
R	5.639983561268	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	14800q4 59200bf4 16650bz4 370d4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1850a4

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 1850a4

-4	8	-3	5	-7	37
14800q4	59200bf4	16650bz4	370d4	90650j4	68450y4

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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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