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SageMath
E = EllipticCurve("gd1")
E.isogeny_class()
Elliptic curves in class 324800gd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 324800.gd2 | 324800gd1 | \([0, -1, 0, -15233, 766337]\) | \(-95443993/5887\) | \(-24113152000000\) | \([2]\) | \(786432\) | \(1.3222\) | \(\Gamma_0(N)\)-optimal |
| 324800.gd1 | 324800gd2 | \([0, -1, 0, -247233, 47398337]\) | \(408023180713/1421\) | \(5820416000000\) | \([2]\) | \(1572864\) | \(1.6688\) |
Rank
sage: E.rank()
The elliptic curves in class 324800gd have rank \(0\).
Complex multiplication
The elliptic curves in class 324800gd do not have complex multiplication.Modular form 324800.2.a.gd
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.
