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	6825k	Isogeny class
Conductor	6825	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	100775390625 = 34 · 59 · 72 · 13	Discriminant
Eigenvalues	1 3- 5- 7+  0 13-  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2451,-44327]	[a1,a2,a3,a4,a6]
j	833237621/51597	j-invariant
L	2.7247445098081	L(r)(E,1)/r!
Ω	0.68118612745202	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	109200ez1 20475be1 6825f1 47775bg1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6825k1

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

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Quadratic twists for elliptic curve 6825k1

-4	-3	5	-7	13
109200ez1	20475be1	6825f1	47775bg1	88725cl1

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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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