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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 14400dr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14400.cl3 | 14400dr1 | \([0, 0, 0, -4575, 119000]\) | \(14526784/15\) | \(10935000000\) | \([2]\) | \(12288\) | \(0.84418\) | \(\Gamma_0(N)\)-optimal |
| 14400.cl2 | 14400dr2 | \([0, 0, 0, -5700, 56000]\) | \(438976/225\) | \(10497600000000\) | \([2, 2]\) | \(24576\) | \(1.1908\) | |
| 14400.cl1 | 14400dr3 | \([0, 0, 0, -50700, -4354000]\) | \(38614472/405\) | \(151165440000000\) | \([2]\) | \(49152\) | \(1.5373\) | |
| 14400.cl4 | 14400dr4 | \([0, 0, 0, 21300, 434000]\) | \(2863288/1875\) | \(-699840000000000\) | \([2]\) | \(49152\) | \(1.5373\) |
Rank
sage: E.rank()
The elliptic curves in class 14400dr have rank \(1\).
Complex multiplication
The elliptic curves in class 14400dr do not have complex multiplication.Modular form 14400.2.a.dr
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.
