Cremona's table of elliptic curves

6825 = 3 · 5² · 7 · 13

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	6825j	Isogeny class
Conductor	6825	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	74069912109375 = 35 · 510 · 74 · 13	Discriminant
Eigenvalues	-1 3- 5+ 7-  0 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-421838,105418917]	[a1,a2,a3,a4,a6]
Generators	[157:6484:1]	Generators of the group modulo torsion
j	531301262949272089/4740474375	j-invariant
L	3.1808664773633	L(r)(E,1)/r!
Ω	0.55261027283636	Real period
R	0.28780377724766	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	109200ct4 20475w3 1365a3 47775q4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6825j3

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	+	-2	-4	0	6	8	-2	-10	-8	-12	6	4	6	-12	12	6	-8	-8	-10	-10

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Quadratic twists for elliptic curve 6825j3

-4	-3	5	-7	13
109200ct4	20475w3	1365a3	47775q4	88725bm4

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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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