Properties

Label 235200i
Number of curves $2$
Conductor $235200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("235200.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 235200i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.i2 235200i1 [0, -1, 0, 8167, -2543463] [2] 1382400 \(\Gamma_0(N)\)-optimal
235200.i1 235200i2 [0, -1, 0, -236833, -42478463] [2] 2764800  

Rank

sage: E.rank()
 

The elliptic curves in class 235200i have rank \(0\).

Modular form 235200.2.a.i

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

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.