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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 12138.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12138.bb1 | 12138ba4 | \([1, 0, 0, -1467837, 684363897]\) | \(14489843500598257/6246072\) | \(150764993878968\) | \([2]\) | \(221184\) | \(2.0632\) | |
| 12138.bb2 | 12138ba3 | \([1, 0, 0, -196237, -17702647]\) | \(34623662831857/14438442312\) | \(348508897558419528\) | \([2]\) | \(221184\) | \(2.0632\) | |
| 12138.bb3 | 12138ba2 | \([1, 0, 0, -92197, 10575425]\) | \(3590714269297/73410624\) | \(1771954002133056\) | \([2, 2]\) | \(110592\) | \(1.7166\) | |
| 12138.bb4 | 12138ba1 | \([1, 0, 0, 283, 495105]\) | \(103823/4386816\) | \(-105887073890304\) | \([2]\) | \(55296\) | \(1.3700\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12138.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 12138.bb do not have complex multiplication.Modular form 12138.2.a.bb
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.
