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	1850b	Isogeny class
Conductor	1850	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	216	Modular degree for the optimal curve
Δ	-59200 = -1 · 26 · 52 · 37	Discriminant
Eigenvalues	2+ -2 5+  0  4  2 -8 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1,-12]	[a1,a2,a3,a4,a6]
Generators	[3:2:1]	Generators of the group modulo torsion
j	-625/2368	j-invariant
L	1.6194188071334	L(r)(E,1)/r!
Ω	1.5950487787824	Real period
R	0.50763927369342	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	14800o1 59200bb1 16650bv1 1850p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1850b1

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	+	0	4	2	-8	-5	-1	10	-4	+	7	9	-6	3	-11	2	-2	14	-3	-11	-8	-2	8

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Quadratic twists for elliptic curve 1850b1

-4	8	-3	5	-7	37
14800o1	59200bb1	16650bv1	1850p1	90650f1	68450bb1

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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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