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Properties

Label 444675cq
Number of curves $2$
Conductor $444675$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cq1")
 
E.isogeny_class()
 

Elliptic curves in class 444675cq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
444675.cq1 444675cq1 \([1, 0, 0, -2671138, 1626242267]\) \(5177717/189\) \(76937167650041015625\) \([2]\) \(12441600\) \(2.5854\) \(\Gamma_0(N)\)-optimal
444675.cq2 444675cq2 \([1, 0, 0, 1034487, 5787659142]\) \(300763/35721\) \(-14541124685857751953125\) \([2]\) \(24883200\) \(2.9320\)  

Rank

sage: E.rank()
 

The elliptic curves in class 444675cq have rank \(1\).

Complex multiplication

The elliptic curves in class 444675cq do not have complex multiplication.

Modular form 444675.2.a.cq

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{6} + 3 q^{8} + q^{9} - q^{12} + 2 q^{13} - q^{16} - 4 q^{17} - q^{18} - 6 q^{19} + O(q^{20})\) 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.