Properties

Label 5445.e
Number of curves $2$
Conductor $5445$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5445.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5445.e1 5445j1 \([1, -1, 1, -122, 344]\) \(205379/75\) \(72772425\) \([2]\) \(1536\) \(0.20893\) \(\Gamma_0(N)\)-optimal
5445.e2 5445j2 \([1, -1, 1, 373, 2126]\) \(5929741/5625\) \(-5457931875\) \([2]\) \(3072\) \(0.55551\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5445.e have rank \(1\).

Complex multiplication

The elliptic curves in class 5445.e do not have complex multiplication.

Modular form 5445.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{5} + 2q^{7} + 3q^{8} - q^{10} - 4q^{13} - 2q^{14} - q^{16} - 6q^{17} + 6q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.