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Properties

Label 45486u
Number of curves $2$
Conductor $45486$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 45486u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
45486.u2 45486u1 \([1, -1, 0, 702, 6772]\) \(145262087/163296\) \(-42974445024\) \([]\) \(69120\) \(0.72678\) \(\Gamma_0(N)\)-optimal
45486.u1 45486u2 \([1, -1, 0, -6993, -333347]\) \(-143719103593/101154816\) \(-26620811771904\) \([]\) \(207360\) \(1.2761\)  

Rank

sage: E.rank()
 

The elliptic curves in class 45486u have rank \(0\).

Complex multiplication

The elliptic curves in class 45486u do not have complex multiplication.

Modular form 45486.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3 q^{5} + q^{7} - q^{8} - 3 q^{10} + 6 q^{11} - 5 q^{13} - q^{14} + q^{16} + 6 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.