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	2550w	Isogeny class
Conductor	2550	Conductor
∏ cp	21	Product of Tamagawa factors cp
deg	1680	Modular degree for the optimal curve
Δ	2550000000 = 27 · 3 · 58 · 17	Discriminant
Eigenvalues	2- 3+ 5- -1 -3  4 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-513,-3969]	[a1,a2,a3,a4,a6]
Generators	[-15:32:1]	Generators of the group modulo torsion
j	38226865/6528	j-invariant
L	3.9205279594746	L(r)(E,1)/r!
Ω	1.0148317631161	Real period
R	0.18396330739668	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	20400dp1 81600ek1 7650bg1 2550l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2550w1

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	-3	4	+	-5	-8	-4	-3	7	2	1	7	-7	-8	-2	11	-6	2	-15	-16	2	-10

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Quadratic twists for elliptic curve 2550w1

-4	8	-3	5	-7	17
20400dp1	81600ek1	7650bg1	2550l1	124950jc1	43350dk1

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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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