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SageMath
E = EllipticCurve("fo1")
E.isogeny_class()
Elliptic curves in class 270480fo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.fo2 | 270480fo1 | \([0, 1, 0, -1569976, 789065444]\) | \(-3552342505518244/179863605135\) | \(-21668631839260277760\) | \([2]\) | \(8110080\) | \(2.4708\) | \(\Gamma_0(N)\)-optimal |
| 270480.fo1 | 270480fo2 | \([0, 1, 0, -25417296, 49313592180]\) | \(7536914291382802562/17961229575\) | \(4327671190055270400\) | \([2]\) | \(16220160\) | \(2.8174\) |
Rank
sage: E.rank()
The elliptic curves in class 270480fo have rank \(2\).
Complex multiplication
The elliptic curves in class 270480fo do not have complex multiplication.Modular form 270480.2.a.fo
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
