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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 10944d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10944.k2 | 10944d1 | \([0, 0, 0, -756, -7776]\) | \(592704/19\) | \(1531809792\) | \([2]\) | \(7680\) | \(0.53669\) | \(\Gamma_0(N)\)-optimal |
| 10944.k1 | 10944d2 | \([0, 0, 0, -1836, 19440]\) | \(1061208/361\) | \(232835088384\) | \([2]\) | \(15360\) | \(0.88326\) |
Rank
sage: E.rank()
The elliptic curves in class 10944d have rank \(1\).
Complex multiplication
The elliptic curves in class 10944d do not have complex multiplication.Modular form 10944.2.a.d
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.
