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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 62400dh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62400.ga2 | 62400dh1 | \([0, 1, 0, -24833, -1317537]\) | \(3307949/468\) | \(239616000000000\) | \([2]\) | \(245760\) | \(1.4851\) | \(\Gamma_0(N)\)-optimal |
62400.ga1 | 62400dh2 | \([0, 1, 0, -104833, 11722463]\) | \(248858189/27378\) | \(14017536000000000\) | \([2]\) | \(491520\) | \(1.8317\) |
Rank
sage: E.rank()
The elliptic curves in class 62400dh have rank \(1\).
Complex multiplication
The elliptic curves in class 62400dh do not have complex multiplication.Modular form 62400.2.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 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.