Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("235200.sd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 235200sd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.sd1 235200sd1 [0, 1, 0, -1177633, 187596863] [2] 6193152 \(\Gamma_0(N)\)-optimal
235200.sd2 235200sd2 [0, 1, 0, 4310367, 1444348863] [2] 12386304  

Rank

sage: E.rank()
 

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

Modular form 235200.2.a.sd

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

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.