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SageMath
sage: E = EllipticCurve("m1")
sage: E.isogeny_class()
Elliptic curves in class 72450.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72450.m1 | 72450bf2 | \([1, -1, 0, -95067, -6265409]\) | \(8341959848041/3327411150\) | \(37901292630468750\) | \([2]\) | \(737280\) | \(1.8793\) | |
| 72450.m2 | 72450bf1 | \([1, -1, 0, -43317, 3411841]\) | \(789145184521/17996580\) | \(204992294062500\) | \([2]\) | \(368640\) | \(1.5328\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 72450.m have rank \(1\).
Complex multiplication
The elliptic curves in class 72450.m do not have complex multiplication.Modular form 72450.2.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.
