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SageMath
E = EllipticCurve("fm1")
E.isogeny_class()
Elliptic curves in class 76050.fm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76050.fm1 | 76050fw4 | \([1, -1, 1, -1259420, -541920193]\) | \(502270291349/1889568\) | \(831113201373156000\) | \([2]\) | \(1228800\) | \(2.2978\) | |
| 76050.fm2 | 76050fw2 | \([1, -1, 1, -80645, 8833907]\) | \(131872229/18\) | \(7917173462250\) | \([2]\) | \(245760\) | \(1.4931\) | |
| 76050.fm3 | 76050fw3 | \([1, -1, 1, -42620, -16262593]\) | \(-19465109/248832\) | \(-109447005942144000\) | \([2]\) | \(614400\) | \(1.9512\) | |
| 76050.fm4 | 76050fw1 | \([1, -1, 1, -4595, 164207]\) | \(-24389/12\) | \(-5278115641500\) | \([2]\) | \(122880\) | \(1.1465\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76050.fm have rank \(0\).
Complex multiplication
The elliptic curves in class 76050.fm do not have complex multiplication.Modular form 76050.2.a.fm
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.
\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
