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	2650d	Isogeny class
Conductor	2650	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-14045000 = -1 · 23 · 54 · 532	Discriminant
Eigenvalues	2+ -1 5-  4  5  0 -7 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,50,-100]	[a1,a2,a3,a4,a6]
Generators	[25:120:1]	Generators of the group modulo torsion
j	21434375/22472	j-invariant
L	2.3103725352245	L(r)(E,1)/r!
Ω	1.2076317551001	Real period
R	0.31885720756999	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	21200y1 84800be1 23850cz1 2650g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2650d1

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	-	4	5	0	-7	-1	-8	-6	6	-10	-9	0	-6	-	-4	-2	9	12	-11	12	-3	3	-18

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Quadratic twists for elliptic curve 2650d1

-4	8	-3	5	-7
21200y1	84800be1	23850cz1	2650g1	129850bd1

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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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