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	6825b	Isogeny class
Conductor	6825	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	20736	Modular degree for the optimal curve
Δ	20664329765625 = 33 · 57 · 73 · 134	Discriminant
Eigenvalues	1 3+ 5+ 7+ -4 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-25525,-1565000]	[a1,a2,a3,a4,a6]
j	117713838907729/1322517105	j-invariant
L	0.75592857100084	L(r)(E,1)/r!
Ω	0.37796428550042	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	109200gk1 20475v1 1365d1 47775cf1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6825b1

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	-	-2	0	0	-10	-4	-10	6	8	-4	10	-12	-10	4	0	-6	0	16	-10	2

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Quadratic twists for elliptic curve 6825b1

-4	-3	5	-7	13
109200gk1	20475v1	1365d1	47775cf1	88725v1

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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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