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	6825l	Isogeny class
Conductor	6825	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	9600	Modular degree for the optimal curve
Δ	180009272625 = 3 · 53 · 75 · 134	Discriminant
Eigenvalues	1 3- 5- 7+ -6 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-4971,132913]	[a1,a2,a3,a4,a6]
j	108647414150813/1440074181	j-invariant
L	2.0325335078178	L(r)(E,1)/r!
Ω	1.0162667539089	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	109200fd1 20475bf1 6825g1 47775bi1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6825l1

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	-	-	+	-6	-	0	2	0	6	-2	-8	-2	8	4	-6	0	6	8	-14	-14	12	12	10	-2

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Quadratic twists for elliptic curve 6825l1

-4	-3	5	-7	13
109200fd1	20475bf1	6825g1	47775bi1	88725cn1

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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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