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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 179088.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179088.m1 | 179088bb2 | \([0, -1, 0, -143977904, -664906437696]\) | \(80584461459025151375298097/333693103021824\) | \(1366806949977391104\) | \([2]\) | \(13271040\) | \(3.1121\) | |
179088.m2 | 179088bb1 | \([0, -1, 0, -8994224, -10397570112]\) | \(-19645130164017251655217/40036908053495808\) | \(-163991175387118829568\) | \([2]\) | \(6635520\) | \(2.7655\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 179088.m have rank \(1\).
Complex multiplication
The elliptic curves in class 179088.m do not have complex multiplication.Modular form 179088.2.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.