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	17760a	Isogeny class
Conductor	17760	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	9715650624000 = 29 · 34 · 53 · 374	Discriminant
Eigenvalues	2+ 3+ 5+  0  0  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-108456,-13710744]	[a1,a2,a3,a4,a6]
Generators	[-11288480845:1025663954:59776471]	Generators of the group modulo torsion
j	275561477457747272/18975880125	j-invariant
L	4.0899565368815	L(r)(E,1)/r!
Ω	0.2630798706773	Real period
R	15.546444227572	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	17760j3 35520cz4 53280br4 88800cd4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17760a2

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

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Quadratic twists for elliptic curve 17760a2

-4	8	-3	5
17760j3	35520cz4	53280br4	88800cd4

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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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