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Properties

Label 90354h
Number of curves $2$
Conductor $90354$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 90354h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
90354.h2 90354h1 \([1, 0, 1, 36934, -1478464]\) \(1586375/1188\) \(-4172825591258148\) \([3]\) \(447552\) \(1.6855\) \(\Gamma_0(N)\)-optimal
90354.h1 90354h2 \([1, 0, 1, -722861, -240965848]\) \(-11892507625/255552\) \(-897621149408419392\) \([]\) \(1342656\) \(2.2348\)  

Rank

sage: E.rank()
 

The elliptic curves in class 90354h have rank \(0\).

Complex multiplication

The elliptic curves in class 90354h do not have complex multiplication.

Modular form 90354.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} - q^{11} + q^{12} - 4 q^{13} + q^{14} + q^{16} - 3 q^{17} - q^{18} + 5 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.