Properties

Label 131760.u
Number of curves $3$
Conductor $131760$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 131760.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
131760.u1 131760r3 \([0, 0, 0, -1037568, -406792528]\) \(-124110120626946048/305\) \(-303575040\) \([]\) \(777600\) \(1.7541\)  
131760.u2 131760r1 \([0, 0, 0, -12768, -561808]\) \(-2081462648832/28372625\) \(-3137785344000\) \([]\) \(259200\) \(1.2048\) \(\Gamma_0(N)\)-optimal
131760.u3 131760r2 \([0, 0, 0, 45792, -2830032]\) \(131716841472/119140625\) \(-9605304000000000\) \([]\) \(777600\) \(1.7541\)  

Rank

sage: E.rank()
 

The elliptic curves in class 131760.u have rank \(0\).

Complex multiplication

The elliptic curves in class 131760.u do not have complex multiplication.

Modular form 131760.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} - 3 q^{11} - 4 q^{13} - 6 q^{17} + 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.