Cremona's table of elliptic curves

2550 = 2 · 3 · 5² · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 17+	Signs for the Atkin-Lehner involutions
Class	2550b	Isogeny class
Conductor	2550	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	474032250000 = 24 · 38 · 56 · 172	Discriminant
Eigenvalues	2+ 3+ 5+  0 -4  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2850,-49500]	[a1,a2,a3,a4,a6]
Generators	[-40:70:1]	Generators of the group modulo torsion
j	163936758817/30338064	j-invariant
L	2.0222602930339	L(r)(E,1)/r!
Ω	0.6617320862709	Real period
R	1.5280053174012	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	20400cx2 81600cn2 7650bz2 102b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2550b2

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	+	4	0	-10	8	2	10	-12	0	-6	12	-10	12	0	-10	-8	-4	-6	14

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Quadratic twists for elliptic curve 2550b2

-4	8	-3	5	-7	17
20400cx2	81600cn2	7650bz2	102b2	124950de2	43350ba2

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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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