Properties

Label 235200baw
Number of curves $4$
Conductor $235200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("baw1")
 
E.isogeny_class()
 

Elliptic curves in class 235200baw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.baw3 235200baw1 \([0, 1, 0, -24908, 1503438]\) \(14526784/15\) \(1764735000000\) \([2]\) \(589824\) \(1.2678\) \(\Gamma_0(N)\)-optimal
235200.baw2 235200baw2 \([0, 1, 0, -31033, 701063]\) \(438976/225\) \(1694145600000000\) \([2, 2]\) \(1179648\) \(1.6144\)  
235200.baw4 235200baw3 \([0, 1, 0, 115967, 5552063]\) \(2863288/1875\) \(-112943040000000000\) \([2]\) \(2359296\) \(1.9610\)  
235200.baw1 235200baw4 \([0, 1, 0, -276033, -55403937]\) \(38614472/405\) \(24395696640000000\) \([2]\) \(2359296\) \(1.9610\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 235200.2.a.baw

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} + 4 q^{11} - 2 q^{13} - 2 q^{17} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.