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
Conductor	6825	Conductor
Count	4	Number of curves in isogeny class
Curves	6825d1 6825d2 6825d3 6825d4	Curves in isogeny class
deg	6144	Modular degree for the optimal curve
Eigenvalues	-1 3+ 5+ 7-  4 13- -6  8	Hecke eigenvalues for primes less than 20
L	2.4188084802488	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	109200ft 20475ba 1365c 47775cj	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for isogeny class 6825d

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 isogeny class 6825d

-4	-3	5	-7	13
109200ft	20475ba	1365c	47775cj	88725f

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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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