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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 72128bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72128.bc2 | 72128bb1 | \([0, 0, 0, 980, 16464]\) | \(13500/23\) | \(-177335631872\) | \([2]\) | \(55296\) | \(0.84341\) | \(\Gamma_0(N)\)-optimal |
| 72128.bc1 | 72128bb2 | \([0, 0, 0, -6860, 170128]\) | \(2315250/529\) | \(8157439066112\) | \([2]\) | \(110592\) | \(1.1900\) |
Rank
sage: E.rank()
The elliptic curves in class 72128bb have rank \(1\).
Complex multiplication
The elliptic curves in class 72128bb do not have complex multiplication.Modular form 72128.2.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 Cremona 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 Cremona labels.
