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SageMath
E = EllipticCurve("ed1")
E.isogeny_class()
Elliptic curves in class 154560.ed
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.ed1 | 154560co4 | \([0, -1, 0, -323265, -70634655]\) | \(14251520160844849/264449745\) | \(69323913953280\) | \([2]\) | \(983040\) | \(1.7808\) | |
| 154560.ed2 | 154560co2 | \([0, -1, 0, -20865, -1022175]\) | \(3832302404449/472410225\) | \(123839506022400\) | \([2, 2]\) | \(491520\) | \(1.4342\) | |
| 154560.ed3 | 154560co1 | \([0, -1, 0, -5185, 128737]\) | \(58818484369/7455105\) | \(1954311045120\) | \([2]\) | \(245760\) | \(1.0876\) | \(\Gamma_0(N)\)-optimal |
| 154560.ed4 | 154560co3 | \([0, -1, 0, 30655, -5318943]\) | \(12152722588271/53476250625\) | \(-14018478243840000\) | \([2]\) | \(983040\) | \(1.7808\) |
Rank
sage: E.rank()
The elliptic curves in class 154560.ed have rank \(1\).
Complex multiplication
The elliptic curves in class 154560.ed do not have complex multiplication.Modular form 154560.2.a.ed
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.
