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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 65520.dh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 65520.dh1 | 65520bf1 | \([0, 0, 0, -4287, 99934]\) | \(46689225424/3901625\) | \(728136864000\) | \([2]\) | \(110592\) | \(1.0181\) | \(\Gamma_0(N)\)-optimal |
| 65520.dh2 | 65520bf2 | \([0, 0, 0, 4533, 458026]\) | \(13799183324/129390625\) | \(-96589584000000\) | \([2]\) | \(221184\) | \(1.3647\) |
Rank
sage: E.rank()
The elliptic curves in class 65520.dh have rank \(1\).
Complex multiplication
The elliptic curves in class 65520.dh do not have complex multiplication.Modular form 65520.2.a.dh
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 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.
