Properties

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

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Show commands: SageMath
E = EllipticCurve("ye1")
 
E.isogeny_class()
 

Elliptic curves in class 235200ye

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.ye1 235200ye1 \([0, 1, 0, -26133, 588363]\) \(1048576/525\) \(988251600000000\) \([2]\) \(884736\) \(1.5700\) \(\Gamma_0(N)\)-optimal
235200.ye2 235200ye2 \([0, 1, 0, 96367, 4630863]\) \(3286064/2205\) \(-66410507520000000\) \([2]\) \(1769472\) \(1.9166\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 235200.2.a.ye

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.