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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 18480.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.ba1 | 18480h3 | \([0, -1, 0, -4936, 135136]\) | \(12990838708516/144375\) | \(147840000\) | \([2]\) | \(12288\) | \(0.72109\) | |
| 18480.ba2 | 18480h2 | \([0, -1, 0, -316, 2080]\) | \(13674725584/1334025\) | \(341510400\) | \([2, 2]\) | \(6144\) | \(0.37452\) | |
| 18480.ba3 | 18480h1 | \([0, -1, 0, -71, -174]\) | \(2508888064/396165\) | \(6338640\) | \([2]\) | \(3072\) | \(0.027946\) | \(\Gamma_0(N)\)-optimal |
| 18480.ba4 | 18480h4 | \([0, -1, 0, 384, 9360]\) | \(6099383804/41507235\) | \(-42503408640\) | \([2]\) | \(12288\) | \(0.72109\) |
Rank
sage: E.rank()
The elliptic curves in class 18480.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 18480.ba do not have complex multiplication.Modular form 18480.2.a.ba
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 LMFDB 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 LMFDB labels.
