Cremona's table of elliptic curves

8470 = 2 · 5 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2+ 5- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	8470k	Isogeny class
Conductor	8470	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	295680	Modular degree for the optimal curve
Δ	-3530675118707660000 = -1 · 25 · 54 · 77 · 118	Discriminant
Eigenvalues	2+  1 5- 7+ 11-  3  0  3	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-4821853,-4076792744]	[a1,a2,a3,a4,a6]
Generators	[107392463770:12508483712926:7645373]	Generators of the group modulo torsion
j	-57839429434456681/16470860000	j-invariant
L	3.8706009348668	L(r)(E,1)/r!
Ω	0.050939966986672	Real period
R	18.995894401931	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	67760ci1 76230do1 42350ck1 59290r1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8470k1

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	-	+	-	3	0	3	-7	8	4	-6	-10	6	-12	-12	-1	-10	-8	8	8	-7	9	6	8

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Quadratic twists for elliptic curve 8470k1

-4	-3	5	-7	-11
67760ci1	76230do1	42350ck1	59290r1	8470bf1

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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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