Cremona's table of elliptic curves

2850 = 2 · 3 · 5² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 19+	Signs for the Atkin-Lehner involutions
Class	2850i	Isogeny class
Conductor	2850	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	126914062500 = 22 · 32 · 510 · 192	Discriminant
Eigenvalues	2+ 3- 5+  0  4 -2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1276,-3802]	[a1,a2,a3,a4,a6]
j	14688124849/8122500	j-invariant
L	1.7109678799834	L(r)(E,1)/r!
Ω	0.85548393999169	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	22800ca2 91200x2 8550x2 570g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2850i2

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	4	-2	-2	+	-4	6	4	6	10	4	12	-6	-12	-2	-4	8	6	-4	12	10	-2

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Quadratic twists for elliptic curve 2850i2

-4	8	-3	5	-19
22800ca2	91200x2	8550x2	570g2	54150bu2

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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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