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Properties

Label 146523ba
Number of curves $2$
Conductor $146523$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 146523ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
146523.t2 146523ba1 \([1, 1, 0, 2740, -55557]\) \(42875/51\) \(-2704542193743\) \([2]\) \(221184\) \(1.0717\) \(\Gamma_0(N)\)-optimal
146523.t1 146523ba2 \([1, 1, 0, -16045, -547724]\) \(8615125/2601\) \(137931651880893\) \([2]\) \(442368\) \(1.4183\)  

Rank

sage: E.rank()
 

The elliptic curves in class 146523ba have rank \(0\).

Complex multiplication

The elliptic curves in class 146523ba do not have complex multiplication.

Modular form 146523.2.a.ba

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{6} - 4 q^{7} - 3 q^{8} + q^{9} + 2 q^{11} + q^{12} - 4 q^{14} - q^{16} + q^{18} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.