Properties

Label 235200.sz
Number of curves $2$
Conductor $235200$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("sz1")
 
E.isogeny_class()
 

Elliptic curves in class 235200.sz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.sz1 235200sz1 \([0, 1, 0, -13368833, 18708734463]\) \(4386781853/27216\) \(1639390814208000000000\) \([2]\) \(14745600\) \(2.9087\) \(\Gamma_0(N)\)-optimal
235200.sz2 235200sz2 \([0, 1, 0, -5528833, 40480414463]\) \(-310288733/11573604\) \(-697150943741952000000000\) \([2]\) \(29491200\) \(3.2553\)  

Rank

sage: E.rank()
 

The elliptic curves in class 235200.sz have rank \(1\).

Complex multiplication

The elliptic curves in class 235200.sz do not have complex multiplication.

Modular form 235200.2.a.sz

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - 2 q^{11} + 2 q^{13} - 8 q^{17} + 2 q^{19} + O(q^{20})\) 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.