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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 28224.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28224.bl1 | 28224cd4 | \([0, 0, 0, -268716, 53546416]\) | \(381775972/567\) | \(3186975742820352\) | \([2]\) | \(196608\) | \(1.8758\) | |
| 28224.bl2 | 28224cd2 | \([0, 0, 0, -21756, 301840]\) | \(810448/441\) | \(619689727770624\) | \([2, 2]\) | \(98304\) | \(1.5292\) | |
| 28224.bl3 | 28224cd1 | \([0, 0, 0, -12936, -562520]\) | \(2725888/21\) | \(1844314665984\) | \([2]\) | \(49152\) | \(1.1826\) | \(\Gamma_0(N)\)-optimal |
| 28224.bl4 | 28224cd3 | \([0, 0, 0, 84084, 2376304]\) | \(11696828/7203\) | \(-40486395547680768\) | \([2]\) | \(196608\) | \(1.8758\) |
Rank
sage: E.rank()
The elliptic curves in class 28224.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 28224.bl do not have complex multiplication.Modular form 28224.2.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.
