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SageMath
E = EllipticCurve("eg1")
E.isogeny_class()
Elliptic curves in class 224400.eg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 224400.eg1 | 224400fz1 | \([0, -1, 0, -35408, 2181312]\) | \(76711450249/12622500\) | \(807840000000000\) | \([2]\) | \(1105920\) | \(1.5820\) | \(\Gamma_0(N)\)-optimal |
| 224400.eg2 | 224400fz2 | \([0, -1, 0, 64592, 12181312]\) | \(465664585751/1274620050\) | \(-81575683200000000\) | \([2]\) | \(2211840\) | \(1.9286\) |
Rank
sage: E.rank()
The elliptic curves in class 224400.eg have rank \(0\).
Complex multiplication
The elliptic curves in class 224400.eg do not have complex multiplication.Modular form 224400.2.a.eg
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
