Cremona's table of elliptic curves

17640 = 2³ · 3² · 5 · 7²

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	17640u	Isogeny class
Conductor	17640	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-6401203200 = -1 · 210 · 36 · 52 · 73	Discriminant
Eigenvalues	2+ 3- 5+ 7- -4  2  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,357,-2842]	[a1,a2,a3,a4,a6]
Generators	[14:70:1]	Generators of the group modulo torsion
j	19652/25	j-invariant
L	4.437188070938	L(r)(E,1)/r!
Ω	0.71530374254188	Real period
R	1.550805555403	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	35280bn1 1960o1 88200gz1 17640bh1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 17640u1

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	2	0	2	4	-10	4	-2	12	-4	-4	-2	-10	6	4	12	-4	-4	-14	-8	-8

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Quadratic twists for elliptic curve 17640u1

-4	-3	5	-7
35280bn1	1960o1	88200gz1	17640bh1

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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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