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	17640w	Isogeny class
Conductor	17640	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	80640	Modular degree for the optimal curve
Δ	-37654757763840 = -1 · 28 · 36 · 5 · 79	Discriminant
Eigenvalues	2+ 3- 5+ 7-  5 -7 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-53508,4773188]	[a1,a2,a3,a4,a6]
Generators	[98:686:1]	Generators of the group modulo torsion
j	-2249728/5	j-invariant
L	4.5552951355348	L(r)(E,1)/r!
Ω	0.65030819793941	Real period
R	0.87560312748034	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	35280bu1 1960m1 88200hi1 17640bk1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 17640w1

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
+	-	+	-	5	-7	-3	2	-8	5	10	4	-6	2	-7	10	-10	12	-2	0	2	-7	4	-8	-17

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Quadratic twists for elliptic curve 17640w1

-4	-3	5	-7
35280bu1	1960m1	88200hi1	17640bk1

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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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