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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 160320.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160320.bs1 | 160320q2 | \([0, 1, 0, -24353921, 46958819199]\) | \(-6093832136609347161121/108676727597808690\) | \(-28488952079399961231360\) | \([]\) | \(12644352\) | \(3.1054\) | |
| 160320.bs2 | 160320q1 | \([0, 1, 0, -94721, -48427521]\) | \(-358531401121921/3652290000000\) | \(-957425909760000000\) | \([]\) | \(1806336\) | \(2.1325\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 160320.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 160320.bs do not have complex multiplication.Modular form 160320.2.a.bs
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
