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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 960d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 960.h3 | 960d1 | \([0, -1, 0, -900, -10098]\) | \(1261112198464/675\) | \(43200\) | \([2]\) | \(384\) | \(0.21907\) | \(\Gamma_0(N)\)-optimal |
| 960.h2 | 960d2 | \([0, -1, 0, -905, -9975]\) | \(20034997696/455625\) | \(1866240000\) | \([2, 2]\) | \(768\) | \(0.56564\) | |
| 960.h1 | 960d3 | \([0, -1, 0, -1985, 19617]\) | \(26410345352/10546875\) | \(345600000000\) | \([4]\) | \(1536\) | \(0.91221\) | |
| 960.h4 | 960d4 | \([0, -1, 0, 95, -31775]\) | \(2863288/13286025\) | \(-435356467200\) | \([2]\) | \(1536\) | \(0.91221\) |
Rank
sage: E.rank()
The elliptic curves in class 960d have rank \(0\).
Complex multiplication
The elliptic curves in class 960d do not have complex multiplication.Modular form 960.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
