Cremona's table of elliptic curves

8288 = 2⁵ · 7 · 37

Field	Data	Notes
Atkin-Lehner	2+ 7- 37+	Signs for the Atkin-Lehner involutions
Class	8288f	Isogeny class
Conductor	8288	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	119040	Modular degree for the optimal curve
Δ	-1452322816 = -1 · 212 · 7 · 373	Discriminant
Eigenvalues	2+  2 -3 7- -5 -7 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3329837,2339853701]	[a1,a2,a3,a4,a6]
j	-996856898790659465728/354571	j-invariant
L	1.2654879391762	L(r)(E,1)/r!
Ω	0.63274396958811	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8288d1 16576v1 74592bq1 58016j1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8288f1

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
+	2	-3	-	-5	-7	-2	0	4	8	1	+	-4	-4	8	1	-1	10	-1	3	12	-2	-14	-3	7

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Quadratic twists for elliptic curve 8288f1

-4	8	-3	-7
8288d1	16576v1	74592bq1	58016j1

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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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