Cremona's table of elliptic curves

1550 = 2 · 5² · 31

Field	Data	Notes
Atkin-Lehner	2+ 5+ 31-	Signs for the Atkin-Lehner involutions
Class	1550d	Isogeny class
Conductor	1550	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-116371093750000 = -1 · 24 · 512 · 313	Discriminant
Eigenvalues	2+  2 5+  4  0  4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,11350,234500]	[a1,a2,a3,a4,a6]
j	10347405816671/7447750000	j-invariant
L	2.2527379979944	L(r)(E,1)/r!
Ω	0.37545633299907	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12400q3 49600ba3 13950cq3 310b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1550d3

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	+	4	0	4	0	-4	6	6	-	-8	-6	10	0	0	-12	14	-8	0	4	8	-6	-18	10

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Quadratic twists for elliptic curve 1550d3

-4	8	-3	5	-7	-31
12400q3	49600ba3	13950cq3	310b3	75950o3	48050e3

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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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