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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 126852.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126852.m1 | 126852n2 | \([0, 1, 0, -1241932, -533114572]\) | \(932410994128/29403\) | \(6680389307505408\) | \([2]\) | \(1843200\) | \(2.1324\) | |
| 126852.m2 | 126852n1 | \([0, 1, 0, -74317, -9088960]\) | \(-3196715008/649539\) | \(-9223492055248944\) | \([2]\) | \(921600\) | \(1.7858\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 126852.m have rank \(1\).
Complex multiplication
The elliptic curves in class 126852.m do not have complex multiplication.Modular form 126852.2.a.m
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.
