Cremona's table of elliptic curves

2450 = 2 · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2+ 5- 7-	Signs for the Atkin-Lehner involutions
Class	2450q	Isogeny class
Conductor	2450	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1080	Modular degree for the optimal curve
Δ	153125000 = 23 · 58 · 72	Discriminant
Eigenvalues	2+  2 5- 7-  0 -2  3 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-200,-1000]	[a1,a2,a3,a4,a6]
Generators	[-11:10:1]	Generators of the group modulo torsion
j	46585/8	j-invariant
L	3.1892780398163	L(r)(E,1)/r!
Ω	1.283571686815	Real period
R	2.4846902378549	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	19600dy1 78400fk1 22050fh1 2450x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2450q1

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	3	-8	-9	-6	-5	8	3	-10	3	6	-12	4	2	-9	10	5	6	-3	-5

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Quadratic twists for elliptic curve 2450q1

-4	8	-3	5	-7
19600dy1	78400fk1	22050fh1	2450x1	2450m1

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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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