Properties

Label 235200bal
Number of curves $4$
Conductor $235200$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bal1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 235200bal

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.bal3 235200bal1 \([0, 1, 0, -44508, -1818762]\) \(82881856/36015\) \(4237128735000000\) \([2]\) \(1769472\) \(1.6947\) \(\Gamma_0(N)\)-optimal
235200.bal2 235200bal2 \([0, 1, 0, -344633, 76513863]\) \(601211584/11025\) \(83013134400000000\) \([2, 2]\) \(3538944\) \(2.0413\)  
235200.bal1 235200bal3 \([0, 1, 0, -5489633, 4948828863]\) \(303735479048/105\) \(6324810240000000\) \([2]\) \(7077888\) \(2.3878\)  
235200.bal4 235200bal4 \([0, 1, 0, -1633, 222288863]\) \(-8/354375\) \(-21346234560000000000\) \([2]\) \(7077888\) \(2.3878\)  

Rank

sage: E.rank()
 

The elliptic curves in class 235200bal have rank \(2\).

Complex multiplication

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

Modular form 235200.2.a.bal

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