Cremona's table of elliptic curves

9570 = 2 · 3 · 5 · 11 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 11- 29-	Signs for the Atkin-Lehner involutions
Class	9570k	Isogeny class
Conductor	9570	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4480	Modular degree for the optimal curve
Δ	631620 = 22 · 32 · 5 · 112 · 29	Discriminant
Eigenvalues	2+ 3- 5+  4 11-  4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-364,-2698]	[a1,a2,a3,a4,a6]
j	5312655169849/631620	j-invariant
L	2.1867559770104	L(r)(E,1)/r!
Ω	1.0933779885052	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	76560bb1 28710bn1 47850ce1 105270bw1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 9570k1

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	-6	2	-2	-	-8	-10	-4	4	-4	14	12	8	10	-4	6	8	12	0	2

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Quadratic twists for elliptic curve 9570k1

-4	-3	5	-11
76560bb1	28710bn1	47850ce1	105270bw1

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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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