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	17640a	Isogeny class
Conductor	17640	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1394620657920 = 28 · 33 · 5 · 79	Discriminant
Eigenvalues	2+ 3+ 5+ 7-  2  2  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-27783,-1781542]	[a1,a2,a3,a4,a6]
j	8503056/5	j-invariant
L	2.9584217395407	L(r)(E,1)/r!
Ω	0.36980271744259	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	35280g2 17640bu2 88200ep2 17640i2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 17640a2

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	2	6	2	4	8	10	10	6	8	8	-14	-4	0	4	6	-10	-16	4	10	10

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Quadratic twists for elliptic curve 17640a2

-4	-3	5	-7
35280g2	17640bu2	88200ep2	17640i2

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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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