Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("235200.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 235200.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.h1 235200h1 [0, -1, 0, -85633, -9600863] [2] 1474560 \(\Gamma_0(N)\)-optimal
235200.h2 235200h2 [0, -1, 0, -57633, -16012863] [2] 2949120  

Rank

sage: E.rank()
 

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

Modular form 235200.2.a.h

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

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.