Cremona's table of elliptic curves

9870 = 2 · 3 · 5 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7- 47+	Signs for the Atkin-Lehner involutions
Class	9870o	Isogeny class
Conductor	9870	Conductor
∏ cp	144	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	14857113600 = 212 · 32 · 52 · 73 · 47	Discriminant
Eigenvalues	2- 3+ 5+ 7-  2 -2  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2916,59109]	[a1,a2,a3,a4,a6]
Generators	[61:-367:1]	Generators of the group modulo torsion
j	2742177603590209/14857113600	j-invariant
L	5.622725643758	L(r)(E,1)/r!
Ω	1.2538010589713	Real period
R	0.12457065841519	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	78960cl1 29610m1 49350y1 69090cc1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 9870o1

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

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Quadratic twists for elliptic curve 9870o1

-4	-3	5	-7
78960cl1	29610m1	49350y1	69090cc1

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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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