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	9735i	Isogeny class
Conductor	9735	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-184517628075 = -1 · 33 · 52 · 113 · 593	Discriminant
Eigenvalues	0 3- 5-  2 11+  5  3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-88495,-10162301]	[a1,a2,a3,a4,a6]
Generators	[3178:33491:8]	Generators of the group modulo torsion
j	-76645175052743704576/184517628075	j-invariant
L	5.1432340699081	L(r)(E,1)/r!
Ω	0.1384010560387	Real period
R	6.1936353872784	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	29205h2 48675a2 107085r2	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 9735i2

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	-	-	2	+	5	3	-4	-9	-6	-4	-10	-3	8	-3	-12	+	2	-4	-6	11	-10	0	-9	8

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Quadratic twists for elliptic curve 9735i2

-3	5	-11
29205h2	48675a2	107085r2

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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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