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SageMath
E = EllipticCurve("fm1")
E.isogeny_class()
Elliptic curves in class 277200fm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.fm4 | 277200fm1 | \([0, 0, 0, 923325, 454653250]\) | \(1865864036231/2993760000\) | \(-139676866560000000000\) | \([2]\) | \(5898240\) | \(2.5507\) | \(\Gamma_0(N)\)-optimal |
| 277200.fm3 | 277200fm2 | \([0, 0, 0, -6276675, 4637853250]\) | \(586145095611769/140040608400\) | \(6533734625510400000000\) | \([2, 2]\) | \(11796480\) | \(2.8972\) | |
| 277200.fm1 | 277200fm3 | \([0, 0, 0, -93756675, 349396533250]\) | \(1953542217204454969/170843779260\) | \(7970887365154560000000\) | \([2]\) | \(23592960\) | \(3.2438\) | |
| 277200.fm2 | 277200fm4 | \([0, 0, 0, -33996675, -72396026750]\) | \(93137706732176569/5369647977540\) | \(250526296040106240000000\) | \([2]\) | \(23592960\) | \(3.2438\) |
Rank
sage: E.rank()
The elliptic curves in class 277200fm have rank \(0\).
Complex multiplication
The elliptic curves in class 277200fm do not have complex multiplication.Modular form 277200.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
