Cremona's table of elliptic curves

16170 = 2 · 3 · 5 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	16170f	Isogeny class
Conductor	16170	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	-37352700 = -1 · 22 · 32 · 52 · 73 · 112	Discriminant
Eigenvalues	2+ 3+ 5+ 7- 11+ -4 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-18,288]	[a1,a2,a3,a4,a6]
Generators	[-6:18:1] [-1:18:1]	Generators of the group modulo torsion
j	-2048383/108900	j-invariant
L	4.3217322684998	L(r)(E,1)/r!
Ω	1.7010081847238	Real period
R	0.31758608712991	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	129360gu1 48510ei1 80850fy1 16170ba1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 16170f1

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
+	+	+	-	+	-4	-6	-6	0	-2	2	-2	-6	-4	-2	-2	-8	8	-12	0	-14	0	-6	-4	-4

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Quadratic twists for elliptic curve 16170f1

-4	-3	5	-7
129360gu1	48510ei1	80850fy1	16170ba1

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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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