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	17640x	Isogeny class
Conductor	17640	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-8472320496864000000 = -1 · 211 · 38 · 56 · 79	Discriminant
Eigenvalues	2+ 3- 5+ 7-  6  2  4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-254163,148473038]	[a1,a2,a3,a4,a6]
Generators	[4034:97497:8]	Generators of the group modulo torsion
j	-30138446/140625	j-invariant
L	5.2695197101877	L(r)(E,1)/r!
Ω	0.2019239463438	Real period
R	6.5241391692291	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	35280bv2 5880ba2 88200hn2 17640bl2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 17640x2

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
+	-	+	-	6	2	4	-8	8	-8	-2	0	-6	-2	-2	-6	-12	-10	2	-12	10	8	-16	10	-10

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Quadratic twists for elliptic curve 17640x2

-4	-3	5	-7
35280bv2	5880ba2	88200hn2	17640bl2

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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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