Cremona's table of elliptic curves

17760 = 2⁵ · 3 · 5 · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 37-	Signs for the Atkin-Lehner involutions
Class	17760v	Isogeny class
Conductor	17760	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	12800	Modular degree for the optimal curve
Δ	492840000 = 26 · 32 · 54 · 372	Discriminant
Eigenvalues	2- 3+ 5- -4  4 -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1850,-30000]	[a1,a2,a3,a4,a6]
j	10946963145664/7700625	j-invariant
L	1.4559129050344	L(r)(E,1)/r!
Ω	0.72795645251719	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	17760r1 35520z2 53280o1 88800p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17760v1

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	4	-2	-2	0	8	6	0	-	2	-8	-8	-6	4	14	4	-8	-6	0	4	14	2

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Quadratic twists for elliptic curve 17760v1

-4	8	-3	5
17760r1	35520z2	53280o1	88800p1

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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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