Cremona's table of elliptic curves

6120 = 2³ · 3² · 5 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	6120r	Isogeny class
Conductor	6120	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2731407428367360 = 210 · 322 · 5 · 17	Discriminant
Eigenvalues	2- 3- 5+  0  0 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-36003,768782]	[a1,a2,a3,a4,a6]
Generators	[227:2072:1]	Generators of the group modulo torsion
j	6913728144004/3658971285	j-invariant
L	3.6985600606443	L(r)(E,1)/r!
Ω	0.39822405335827	Real period
R	4.6438180082969	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	12240g3 48960ck4 2040c3 30600t4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6120r3

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

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Quadratic twists for elliptic curve 6120r3

-4	8	-3	5	17
12240g3	48960ck4	2040c3	30600t4	104040co4

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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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