Cremona's table of elliptic curves

9735 = 3 · 5 · 11 · 59

Field	Data	Notes
Atkin-Lehner	3- 5+ 11+ 59+	Signs for the Atkin-Lehner involutions
Class	9735f	Isogeny class
Conductor	9735	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	57600	Modular degree for the optimal curve
Δ	2705845531640625 = 36 · 58 · 115 · 59	Discriminant
Eigenvalues	1 3- 5+ -2 11+  2 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-203584,35250257]	[a1,a2,a3,a4,a6]
j	933150245933942596729/2705845531640625	j-invariant
L	1.3683539247277	L(r)(E,1)/r!
Ω	0.45611797490924	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	29205q1 48675c1 107085n1	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 9735f1

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
1	-	+	-2	+	2	-4	-6	-4	0	-6	2	4	8	-4	-2	+	6	10	8	-6	-6	12	16	-2

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Quadratic twists for elliptic curve 9735f1

-3	5	-11
29205q1	48675c1	107085n1

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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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