Properties

Label 145728.dv
Number of curves $2$
Conductor $145728$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dv1")
 
E.isogeny_class()
 

Elliptic curves in class 145728.dv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
145728.dv1 145728fj2 \([0, 0, 0, -713100, 229975792]\) \(209849322390625/1882056627\) \(359666622420221952\) \([2]\) \(1310720\) \(2.1915\)  
145728.dv2 145728fj1 \([0, 0, 0, -13260, 8546416]\) \(-1349232625/164333367\) \(-31404595489800192\) \([2]\) \(655360\) \(1.8449\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 145728.dv have rank \(1\).

Complex multiplication

The elliptic curves in class 145728.dv do not have complex multiplication.

Modular form 145728.2.a.dv

sage: E.q_eigenform(10)
 
\(q - 2 q^{7} + q^{11} - 2 q^{13} - 2 q^{19} + O(q^{20})\) 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 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.