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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 346560.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346560.b1 | 346560b3 | \([0, -1, 0, -70236641, 226588880001]\) | \(3107086841064961/570\) | \(7029693394452480\) | \([2]\) | \(26542080\) | \(2.8765\) | |
| 346560.b2 | 346560b4 | \([0, -1, 0, -5083361, 2348756865]\) | \(1177918188481/488703750\) | \(6027083374068695040000\) | \([2]\) | \(26542080\) | \(2.8765\) | |
| 346560.b3 | 346560b2 | \([0, -1, 0, -4390241, 3540784641]\) | \(758800078561/324900\) | \(4006925234837913600\) | \([2, 2]\) | \(13271040\) | \(2.5299\) | |
| 346560.b4 | 346560b1 | \([0, -1, 0, -231521, 73243905]\) | \(-111284641/123120\) | \(-1518413773201735680\) | \([2]\) | \(6635520\) | \(2.1833\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 346560.b have rank \(1\).
Complex multiplication
The elliptic curves in class 346560.b do not have complex multiplication.Modular form 346560.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
