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	1850f	Isogeny class
Conductor	1850	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	87616000 = 29 · 53 · 372	Discriminant
Eigenvalues	2+  0 5-  2  0 -2  6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-13657,-610899]	[a1,a2,a3,a4,a6]
Generators	[2199:101853:1]	Generators of the group modulo torsion
j	2253707317528029/700928	j-invariant
L	2.2592462496032	L(r)(E,1)/r!
Ω	0.44163068883084	Real period
R	5.1156912477805	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	14800bh2 59200bm2 16650cr2 1850o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1850f2

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

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Quadratic twists for elliptic curve 1850f2

-4	8	-3	5	-7	37
14800bh2	59200bm2	16650cr2	1850o2	90650bh2	68450bi2

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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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