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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 32760.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32760.bp1 | 32760ba1 | \([0, 0, 0, -1872387, -928873234]\) | \(26257105115938658412/1713748278480875\) | \(47381712403439232000\) | \([2]\) | \(921600\) | \(2.5253\) | \(\Gamma_0(N)\)-optimal |
| 32760.bp2 | 32760ba2 | \([0, 0, 0, 1554933, -3946971226]\) | \(7519085745831768474/126058993542015625\) | \(-6970558106899296000000\) | \([2]\) | \(1843200\) | \(2.8719\) |
Rank
sage: E.rank()
The elliptic curves in class 32760.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 32760.bp do not have complex multiplication.Modular form 32760.2.a.bp
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
