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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 143650f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 143650.bf2 | 143650f1 | \([1, 1, 1, 1685687, -260808969]\) | \(7023836099951/4456448000\) | \(-336100364288000000000\) | \([]\) | \(4717440\) | \(2.6277\) | \(\Gamma_0(N)\)-optimal |
| 143650.bf1 | 143650f2 | \([1, 1, 1, -28058313, -59061992969]\) | \(-32391289681150609/1228250000000\) | \(-92633252410156250000000\) | \([]\) | \(14152320\) | \(3.1770\) |
Rank
sage: E.rank()
The elliptic curves in class 143650f have rank \(1\).
Complex multiplication
The elliptic curves in class 143650f do not have complex multiplication.Modular form 143650.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
