Cremona's table of elliptic curves

12045 = 3 · 5 · 11 · 73

Field	Data	Notes
Atkin-Lehner	3+ 5- 11- 73+	Signs for the Atkin-Lehner involutions
Class	12045b	Isogeny class
Conductor	12045	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	8208	Modular degree for the optimal curve
Δ	9562296645 = 39 · 5 · 113 · 73	Discriminant
Eigenvalues	0 3+ 5-  0 11-  6  3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1055,-11977]	[a1,a2,a3,a4,a6]
Generators	[-17:27:1]	Generators of the group modulo torsion
j	129984832700416/9562296645	j-invariant
L	3.6170735865408	L(r)(E,1)/r!
Ω	0.84152137122597	Real period
R	1.4327517241269	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	36135e1 60225v1	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 12045b1

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	-	6	3	-4	-5	-4	-8	8	-5	6	4	6	-9	0	10	-10	+	-16	1	-8	16

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Quadratic twists for elliptic curve 12045b1

-3	5
36135e1	60225v1

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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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