Cremona's table of elliptic curves

2650 = 2 · 5² · 53

Field	Data	Notes
Atkin-Lehner	2- 5+ 53+	Signs for the Atkin-Lehner involutions
Class	2650k	Isogeny class
Conductor	2650	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	60480	Modular degree for the optimal curve
Δ	-9863101250000000 = -1 · 27 · 510 · 534	Discriminant
Eigenvalues	2-  3 5+  2 -3 -4  3  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-547305,156054697]	[a1,a2,a3,a4,a6]
j	-1856569331248425/1009981568	j-invariant
L	5.6413552991352	L(r)(E,1)/r!
Ω	0.40295394993823	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	21200n1 84800ba1 23850ba1 2650e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2650k1

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
-	3	+	2	-3	-4	3	1	6	-4	10	-10	1	4	0	+	0	10	1	12	-7	-14	-11	-1	-18

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Quadratic twists for elliptic curve 2650k1

-4	8	-3	5	-7
21200n1	84800ba1	23850ba1	2650e1	129850cm1

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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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