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	6825f	Isogeny class
Conductor	6825	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-970207875 = -1 · 38 · 53 · 7 · 132	Discriminant
Eigenvalues	-1 3+ 5- 7-  0 13+ -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,77,-1444]	[a1,a2,a3,a4,a6]
Generators	[25:117:1]	Generators of the group modulo torsion
j	403583419/7761663	j-invariant
L	2.1605262758853	L(r)(E,1)/r!
Ω	0.76158924315627	Real period
R	1.4184327675975	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	109200go2 20475bg2 6825k2 47775dn2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6825f2

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 6825f2

-4	-3	5	-7	13
109200go2	20475bg2	6825k2	47775dn2	88725bd2

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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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