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	6825g	Isogeny class
Conductor	6825	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	48000	Modular degree for the optimal curve
Δ	2812644884765625 = 3 · 59 · 75 · 134	Discriminant
Eigenvalues	-1 3+ 5- 7- -6 13+  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-124263,16614156]	[a1,a2,a3,a4,a6]
Generators	[60:3032:1]	Generators of the group modulo torsion
j	108647414150813/1440074181	j-invariant
L	1.9627751101208	L(r)(E,1)/r!
Ω	0.45448830900267	Real period
R	0.86372963671075	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	109200gv1 20475bh1 6825l1 47775dp1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6825g1

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 6825g1

-4	-3	5	-7	13
109200gv1	20475bh1	6825l1	47775dp1	88725be1

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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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