Cremona's table of elliptic curves

17700 = 2² · 3 · 5² · 59

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 59+	Signs for the Atkin-Lehner involutions
Class	17700k	Isogeny class
Conductor	17700	Conductor
∏ cp	28	Product of Tamagawa factors cp
Δ	152258940000000 = 28 · 37 · 57 · 592	Discriminant
Eigenvalues	2- 3- 5+  0  0  4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1457508,-677760012]	[a1,a2,a3,a4,a6]
Generators	[12474:232275:8]	Generators of the group modulo torsion
j	85604552312875216/38064735	j-invariant
L	6.3064808362775	L(r)(E,1)/r!
Ω	0.13740318653941	Real period
R	6.5568045141043	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	70800z2 53100j2 3540c2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 17700k2

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	4	-2	0	-2	-6	-2	4	-6	4	-6	-10	+	14	-4	-16	12	4	6	-12	0

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Quadratic twists for elliptic curve 17700k2

-4	-3	5
70800z2	53100j2	3540c2

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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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