Properties

Label 93600.cu
Number of curves $4$
Conductor $93600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cu1")
 
E.isogeny_class()
 

Elliptic curves in class 93600.cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.cu1 93600u4 \([0, 0, 0, -842475, -297634750]\) \(11339065490696/351\) \(2047032000000\) \([2]\) \(786432\) \(1.8667\)  
93600.cu2 93600u3 \([0, 0, 0, -83100, 1316000]\) \(1360251712/771147\) \(35978634432000000\) \([2]\) \(786432\) \(1.8667\)  
93600.cu3 93600u1 \([0, 0, 0, -52725, -4637500]\) \(22235451328/123201\) \(89813529000000\) \([2, 2]\) \(393216\) \(1.5202\) \(\Gamma_0(N)\)-optimal
93600.cu4 93600u2 \([0, 0, 0, -23475, -9756250]\) \(-245314376/6908733\) \(-40291730856000000\) \([2]\) \(786432\) \(1.8667\)  

Rank

sage: E.rank()
 

The elliptic curves in class 93600.cu have rank \(0\).

Complex multiplication

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

Modular form 93600.2.a.cu

sage: E.q_eigenform(10)
 
\(q + 4 q^{11} - q^{13} - 6 q^{17} + 8 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.