Properties

Label 93600bx
Number of curves $4$
Conductor $93600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 93600bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.h3 93600bx1 \([0, 0, 0, -19425, 713000]\) \(1111934656/342225\) \(249482025000000\) \([2, 2]\) \(294912\) \(1.4672\) \(\Gamma_0(N)\)-optimal
93600.h4 93600bx2 \([0, 0, 0, 53700, 4808000]\) \(367061696/426465\) \(-19897151040000000\) \([2]\) \(589824\) \(1.8138\)  
93600.h2 93600bx3 \([0, 0, 0, -120675, -15588250]\) \(33324076232/1285245\) \(7495548840000000\) \([2]\) \(589824\) \(1.8138\)  
93600.h1 93600bx4 \([0, 0, 0, -282675, 57838250]\) \(428320044872/73125\) \(426465000000000\) \([2]\) \(589824\) \(1.8138\)  

Rank

sage: E.rank()
 

The elliptic curves in class 93600bx have rank \(1\).

Complex multiplication

The elliptic curves in class 93600bx do not have complex multiplication.

Modular form 93600.2.a.bx

sage: E.q_eigenform(10)
 
\(q - 4q^{7} - 4q^{11} + q^{13} + 2q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.