Cremona's table of elliptic curves

6225 = 3 · 5² · 83

Field	Data	Notes
Atkin-Lehner	3- 5+ 83-	Signs for the Atkin-Lehner involutions
Class	6225h	Isogeny class
Conductor	6225	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	-35015625 = -1 · 33 · 56 · 83	Discriminant
Eigenvalues	1 3- 5+  0 -3  6  4 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1376,19523]	[a1,a2,a3,a4,a6]
Generators	[21:-8:1]	Generators of the group modulo torsion
j	-18420660721/2241	j-invariant
L	5.6716550157358	L(r)(E,1)/r!
Ω	1.986559067042	Real period
R	0.95167151245445	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	99600bn1 18675i1 249a1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 6225h1

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

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Quadratic twists for elliptic curve 6225h1

-4	-3	5
99600bn1	18675i1	249a1

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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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