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
deg	1536	Modular degree for the optimal curve
Δ	6449625 = 34 · 53 · 72 · 13	Discriminant
Eigenvalues	-1 3+ 5- 7-  0 13+ -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-98,-394]	[a1,a2,a3,a4,a6]
Generators	[-6:7:1]	Generators of the group modulo torsion
j	833237621/51597	j-invariant
L	2.1605262758853	L(r)(E,1)/r!
Ω	1.5231784863125	Real period
R	0.70921638379876	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	109200go1 20475bg1 6825k1 47775dn1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6825f1

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 6825f1

-4	-3	5	-7	13
109200go1	20475bg1	6825k1	47775dn1	88725bd1

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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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