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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 5520.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5520.bb1 | 5520bg2 | \([0, 1, 0, -3880, 91700]\) | \(1577505447721/838350\) | \(3433881600\) | \([2]\) | \(6912\) | \(0.77950\) | |
| 5520.bb2 | 5520bg1 | \([0, 1, 0, -200, 1908]\) | \(-217081801/285660\) | \(-1170063360\) | \([2]\) | \(3456\) | \(0.43292\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5520.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 5520.bb do not have complex multiplication.Modular form 5520.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
