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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 366300bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 366300.bb2 | 366300bb1 | \([0, 0, 0, -100387200, 383527164125]\) | \(613890903731775471616/6595847815409325\) | \(1202093264358349481250000\) | \([2]\) | \(46006272\) | \(3.4361\) | \(\Gamma_0(N)\)-optimal |
| 366300.bb1 | 366300bb2 | \([0, 0, 0, -181579575, -325201077250]\) | \(227058193522061599696/115731900414961875\) | \(337474221610028827500000000\) | \([2]\) | \(92012544\) | \(3.7827\) |
Rank
sage: E.rank()
The elliptic curves in class 366300bb have rank \(1\).
Complex multiplication
The elliptic curves in class 366300bb do not have complex multiplication.Modular form 366300.2.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.
