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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 340032bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 340032.bt2 | 340032bt1 | \([0, -1, 0, -24087276353, -1438934300537535]\) | \(-5895856113332931416918127084625/215771481613620039647232\) | \(-56563199276120811673283985408\) | \([]\) | \(574801920\) | \(4.6049\) | \(\Gamma_0(N)\)-optimal |
| 340032.bt1 | 340032bt2 | \([0, -1, 0, -1951086521153, -1048968960286110399]\) | \(-3133382230165522315000208250857964625/153574604080128\) | \(-40258661011981074432\) | \([]\) | \(1724405760\) | \(5.1542\) |
Rank
sage: E.rank()
The elliptic curves in class 340032bt have rank \(1\).
Complex multiplication
The elliptic curves in class 340032bt do not have complex multiplication.Modular form 340032.2.a.bt
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.
