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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 55440.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55440.f1 | 55440g4 | \([0, 0, 0, -147843, 21880098]\) | \(239369344910082/385\) | \(574801920\) | \([2]\) | \(131072\) | \(1.3740\) | |
| 55440.f2 | 55440g3 | \([0, 0, 0, -11763, 140562]\) | \(120564797922/64054375\) | \(95632669440000\) | \([2]\) | \(131072\) | \(1.3740\) | |
| 55440.f3 | 55440g2 | \([0, 0, 0, -9243, 341658]\) | \(116986321764/148225\) | \(110649369600\) | \([2, 2]\) | \(65536\) | \(1.0275\) | |
| 55440.f4 | 55440g1 | \([0, 0, 0, -423, 8262]\) | \(-44851536/132055\) | \(-24644632320\) | \([2]\) | \(32768\) | \(0.68090\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 55440.f have rank \(2\).
Complex multiplication
The elliptic curves in class 55440.f do not have complex multiplication.Modular form 55440.2.a.f
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.
