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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 480240do
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
480240.do1 | 480240do1 | \([0, 0, 0, -53787, 4801034]\) | \(5763259856089/450225\) | \(1344364646400\) | \([2]\) | \(884736\) | \(1.3745\) | \(\Gamma_0(N)\)-optimal |
480240.do2 | 480240do2 | \([0, 0, 0, -50187, 5471354]\) | \(-4681768588489/1621620405\) | \(-4842132583403520\) | \([2]\) | \(1769472\) | \(1.7211\) |
Rank
sage: E.rank()
The elliptic curves in class 480240do have rank \(0\).
Complex multiplication
The elliptic curves in class 480240do do not have complex multiplication.Modular form 480240.2.a.do
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.