Properties

Label 235200g
Number of curves 2
Conductor 235200
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("235200.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 235200g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.g1 235200g1 [0, -1, 0, -56513, 5024097] [2] 1179648 \(\Gamma_0(N)\)-optimal
235200.g2 235200g2 [0, -1, 0, 21887, 17803297] [2] 2359296  

Rank

sage: E.rank()
 

The elliptic curves in class 235200g have rank \(2\).

Modular form 235200.2.a.g

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

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 Cremona 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 Cremona labels.