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	1550b	Isogeny class
Conductor	1550	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	216	Modular degree for the optimal curve
Δ	-12300800 = -1 · 29 · 52 · 312	Discriminant
Eigenvalues	2+  1 5+  0 -1  0  1 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-31,178]	[a1,a2,a3,a4,a6]
Generators	[-4:17:1]	Generators of the group modulo torsion
j	-125768785/492032	j-invariant
L	2.3977577607551	L(r)(E,1)/r!
Ω	1.9668421648633	Real period
R	0.60954503711328	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	12400v1 49600g1 13950cd1 1550g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1550b1

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
+	1	+	0	-1	0	1	-7	4	-4	+	-4	-3	4	-6	-2	-4	-6	5	-6	3	-10	15	9	-10

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Quadratic twists for elliptic curve 1550b1

-4	8	-3	5	-7	-31
12400v1	49600g1	13950cd1	1550g1	75950ba1	48050c1

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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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