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	1550c	Isogeny class
Conductor	1550	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-19375000000 = -1 · 26 · 510 · 31	Discriminant
Eigenvalues	2+ -2 5+  0  2  0 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1651,-26802]	[a1,a2,a3,a4,a6]
Generators	[87:656:1]	Generators of the group modulo torsion
j	-31824875809/1240000	j-invariant
L	1.5376897099941	L(r)(E,1)/r!
Ω	0.37365703802845	Real period
R	2.05762176742	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	12400x1 49600j1 13950ce1 310a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1550c1

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	2	0	-2	-4	4	-4	+	8	6	-2	0	-8	8	0	-4	0	-6	-4	-6	-6	2

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Quadratic twists for elliptic curve 1550c1

-4	8	-3	5	-7	-31
12400x1	49600j1	13950ce1	310a1	75950bc1	48050d1

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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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