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	2550v	Isogeny class
Conductor	2550	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	12393000000 = 26 · 36 · 56 · 17	Discriminant
Eigenvalues	2- 3+ 5+ -2  0 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-6388,193781]	[a1,a2,a3,a4,a6]
Generators	[41:33:1]	Generators of the group modulo torsion
j	1845026709625/793152	j-invariant
L	3.8538315556177	L(r)(E,1)/r!
Ω	1.2459661389616	Real period
R	0.51550779686913	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	20400dk1 81600dw1 7650p1 102c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2550v1

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	-	-4	6	0	-10	-8	6	4	-12	-6	-12	8	4	6	-2	-10	-12	-18	-14

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Quadratic twists for elliptic curve 2550v1

-4	8	-3	5	-7	17
20400dk1	81600dw1	7650p1	102c1	124950hi1	43350cy1

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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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