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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 480960cl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
480960.cl2 | 480960cl1 | \([0, 0, 0, -5388, 95728]\) | \(2444008923/855040\) | \(6051877355520\) | \([2]\) | \(614400\) | \(1.1540\) | \(\Gamma_0(N)\)-optimal |
480960.cl1 | 480960cl2 | \([0, 0, 0, -36108, -2570768]\) | \(735580702683/22311200\) | \(157916174745600\) | \([2]\) | \(1228800\) | \(1.5006\) |
Rank
sage: E.rank()
The elliptic curves in class 480960cl have rank \(1\).
Complex multiplication
The elliptic curves in class 480960cl do not have complex multiplication.Modular form 480960.2.a.cl
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.