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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 223146di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 223146.bh2 | 223146di1 | \([1, -1, 0, -165976388622, -26027389979926700]\) | \(-5895856113332931416918127084625/215771481613620039647232\) | \(-18505883000423011568409297027072\) | \([]\) | \(1149603840\) | \(5.0874\) | \(\Gamma_0(N)\)-optimal |
| 223146.bh1 | 223146di2 | \([1, -1, 0, -13444205559822, -18973644225303608492]\) | \(-3133382230165522315000208250857964625/153574604080128\) | \(-13171498076063351743488\) | \([]\) | \(3448811520\) | \(5.6367\) |
Rank
sage: E.rank()
The elliptic curves in class 223146di have rank \(1\).
Complex multiplication
The elliptic curves in class 223146di do not have complex multiplication.Modular form 223146.2.a.di
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.
