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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 254100.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254100.bb1 | 254100bb1 | \([0, -1, 0, -52158058, -146518461263]\) | \(-35431687725461248/440311012911\) | \(-195009454585906017750000\) | \([]\) | \(41990400\) | \(3.2794\) | \(\Gamma_0(N)\)-optimal |
| 254100.bb2 | 254100bb2 | \([0, -1, 0, 181432442, -748912423763]\) | \(1491325446082364672/1410025768453071\) | \(-624486665096622728457750000\) | \([]\) | \(125971200\) | \(3.8287\) |
Rank
sage: E.rank()
The elliptic curves in class 254100.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 254100.bb do not have complex multiplication.Modular form 254100.2.a.bb
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
