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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 230640dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 230640.dc2 | 230640dc1 | \([0, 1, 0, 38120, -41851372]\) | \(1685159/209250\) | \(-760668754940928000\) | \([]\) | \(2764800\) | \(2.1104\) | \(\Gamma_0(N)\)-optimal |
| 230640.dc1 | 230640dc2 | \([0, 1, 0, -8034280, -8769730252]\) | \(-15777367606441/3574920\) | \(-12995603084413009920\) | \([]\) | \(8294400\) | \(2.6597\) |
Rank
sage: E.rank()
The elliptic curves in class 230640dc have rank \(1\).
Complex multiplication
The elliptic curves in class 230640dc do not have complex multiplication.Modular form 230640.2.a.dc
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
