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Properties

Label 333270.cu
Number of curves $2$
Conductor $333270$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("cu1")
 
E.isogeny_class()
 

Elliptic curves in class 333270.cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.cu1 333270cu2 \([1, -1, 1, -730163723, -7593954577603]\) \(32787357410490047/4961250\) \(6514321139787132078750\) \([2]\) \(108527616\) \(3.5918\)  
333270.cu2 333270cu1 \([1, -1, 1, -45769973, -117911010103]\) \(8075838390047/98437500\) \(129252403567205001562500\) \([2]\) \(54263808\) \(3.2453\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 333270.cu have rank \(0\).

Complex multiplication

The elliptic curves in class 333270.cu do not have complex multiplication.

Modular form 333270.2.a.cu

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} - 6 q^{11} - q^{14} + q^{16} + 2 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.