Properties

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

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Show commands: SageMath
E = EllipticCurve("do1")
 
E.isogeny_class()
 

Elliptic curves in class 235200do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.do1 235200do1 \([0, -1, 0, -2770133, 1775465637]\) \(1248870793216/42525\) \(80048379600000000\) \([2]\) \(4423680\) \(2.3351\) \(\Gamma_0(N)\)-optimal
235200.do2 235200do2 \([0, -1, 0, -2647633, 1939493137]\) \(-68150496976/14467005\) \(-435719339838720000000\) \([2]\) \(8847360\) \(2.6817\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 235200.2.a.do

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