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SageMath
E = EllipticCurve("fn1")
E.isogeny_class()
Elliptic curves in class 91200.fn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91200.fn1 | 91200dd4 | \([0, 1, 0, -741169633, 4959021012863]\) | \(10993009831928446009969/3767761230468750000\) | \(15432750000000000000000000000\) | \([2]\) | \(79626240\) | \(4.1108\) | |
| 91200.fn2 | 91200dd2 | \([0, 1, 0, -663985633, 6585238356863]\) | \(7903870428425797297009/886464000000\) | \(3630956544000000000000\) | \([2]\) | \(26542080\) | \(3.5615\) | |
| 91200.fn3 | 91200dd1 | \([0, 1, 0, -41393633, 103433044863]\) | \(-1914980734749238129/20440940544000\) | \(-83726092468224000000000\) | \([2]\) | \(13271040\) | \(3.2149\) | \(\Gamma_0(N)\)-optimal |
| 91200.fn4 | 91200dd3 | \([0, 1, 0, 136782367, 538532692863]\) | \(69096190760262356111/70568821500000000\) | \(-289049892864000000000000000\) | \([2]\) | \(39813120\) | \(3.7642\) |
Rank
sage: E.rank()
The elliptic curves in class 91200.fn have rank \(0\).
Complex multiplication
The elliptic curves in class 91200.fn do not have complex multiplication.Modular form 91200.2.a.fn
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
