Cremona's table of elliptic curves

6045 = 3 · 5 · 13 · 31

Field	Data	Notes
Atkin-Lehner	3- 5+ 13- 31-	Signs for the Atkin-Lehner involutions
Class	6045j	Isogeny class
Conductor	6045	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	16800	Modular degree for the optimal curve
Δ	-175646764200375 = -1 · 320 · 53 · 13 · 31	Discriminant
Eigenvalues	1 3- 5+  0  4 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-18634,1166807]	[a1,a2,a3,a4,a6]
j	-715498095288059929/175646764200375	j-invariant
L	2.7195475847452	L(r)(E,1)/r!
Ω	0.54390951694903	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	96720bj1 18135u1 30225h1 78585q1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6045j1

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

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Quadratic twists for elliptic curve 6045j1

-4	-3	5	13
96720bj1	18135u1	30225h1	78585q1

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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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