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SageMath
E = EllipticCurve("fn1")
E.isogeny_class()
Elliptic curves in class 73920.fn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.fn1 | 73920co6 | \([0, 1, 0, -8213441, -9062897505]\) | \(467508233804095622882/315748125\) | \(41385738240000\) | \([2]\) | \(1572864\) | \(2.3627\) | |
| 73920.fn2 | 73920co4 | \([0, 1, 0, -513441, -141677505]\) | \(228410605013945764/187597265625\) | \(12294374400000000\) | \([2, 2]\) | \(786432\) | \(2.0161\) | |
| 73920.fn3 | 73920co5 | \([0, 1, 0, -402561, -204457761]\) | \(-55043996611705922/105743408203125\) | \(-13860000000000000000\) | \([2]\) | \(1572864\) | \(2.3627\) | |
| 73920.fn4 | 73920co3 | \([0, 1, 0, -333121, 73080479]\) | \(62380825826921284/787768887675\) | \(51627221822668800\) | \([2]\) | \(786432\) | \(2.0161\) | |
| 73920.fn5 | 73920co2 | \([0, 1, 0, -39121, -1183921]\) | \(404151985581136/197735855625\) | \(3239704258560000\) | \([2, 2]\) | \(393216\) | \(1.6695\) | |
| 73920.fn6 | 73920co1 | \([0, 1, 0, 8899, -137085]\) | \(76102438406144/52315569075\) | \(-53571142732800\) | \([2]\) | \(196608\) | \(1.3229\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 73920.fn have rank \(1\).
Complex multiplication
The elliptic curves in class 73920.fn do not have complex multiplication.Modular form 73920.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
