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	6825d	Isogeny class
Conductor	6825	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	7998046875 = 32 · 510 · 7 · 13	Discriminant
Eigenvalues	-1 3+ 5+ 7-  4 13- -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-109213,-13937344]	[a1,a2,a3,a4,a6]
Generators	[3470:34511:8]	Generators of the group modulo torsion
j	9219915604149769/511875	j-invariant
L	2.4188084802488	L(r)(E,1)/r!
Ω	0.26262190734467	Real period
R	4.6051155912793	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	109200ft4 20475ba3 1365c3 47775cj4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6825d3

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

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Quadratic twists for elliptic curve 6825d3

-4	-3	5	-7	13
109200ft4	20475ba3	1365c3	47775cj4	88725f4

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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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