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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 85008bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85008.r2 | 85008bi1 | \([0, -1, 0, -6021819088, 179869798476736]\) | \(-5895856113332931416918127084625/215771481613620039647232\) | \(-883799988689387682395062272\) | \([]\) | \(71850240\) | \(4.2583\) | \(\Gamma_0(N)\)-optimal |
| 85008.r1 | 85008bi2 | \([0, -1, 0, -487771630288, 131121363921578944]\) | \(-3133382230165522315000208250857964625/153574604080128\) | \(-629041578312204288\) | \([]\) | \(215550720\) | \(4.8076\) |
Rank
sage: E.rank()
The elliptic curves in class 85008bi have rank \(0\).
Complex multiplication
The elliptic curves in class 85008bi do not have complex multiplication.Modular form 85008.2.a.bi
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.
