Cremona's table of elliptic curves

8246 = 2 · 7 · 19 · 31

Field	Data	Notes
Atkin-Lehner	2- 7- 19- 31+	Signs for the Atkin-Lehner involutions
Class	8246f	Isogeny class
Conductor	8246	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	138240	Modular degree for the optimal curve
Δ	-358099560571611376 = -1 · 24 · 78 · 194 · 313	Discriminant
Eigenvalues	2-  0 -2 7-  4 -2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1155061,478965501]	[a1,a2,a3,a4,a6]
j	-170426890729814954542497/358099560571611376	j-invariant
L	2.4239916082864	L(r)(E,1)/r!
Ω	0.3029989510358	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	65968j1 74214m1 57722p1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 8246f1

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

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Quadratic twists for elliptic curve 8246f1

-4	-3	-7
65968j1	74214m1	57722p1

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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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