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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 190463.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190463.bl1 | 190463bl4 | \([1, -1, 0, -1024256, -398642035]\) | \(209267191953/55223\) | \(31359443705460143\) | \([2]\) | \(1843200\) | \(2.1498\) | |
| 190463.bl2 | 190463bl2 | \([1, -1, 0, -71941, -4574088]\) | \(72511713/25921\) | \(14719738882154761\) | \([2, 2]\) | \(921600\) | \(1.8032\) | |
| 190463.bl3 | 190463bl1 | \([1, -1, 0, -30536, 2009307]\) | \(5545233/161\) | \(91426949578601\) | \([2]\) | \(460800\) | \(1.4566\) | \(\Gamma_0(N)\)-optimal |
| 190463.bl4 | 190463bl3 | \([1, -1, 0, 217894, -32340281]\) | \(2014698447/1958887\) | \(-1112391695522838367\) | \([2]\) | \(1843200\) | \(2.1498\) |
Rank
sage: E.rank()
The elliptic curves in class 190463.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 190463.bl do not have complex multiplication.Modular form 190463.2.a.bl
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.
