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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 3024.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3024.bb1 | 3024o3 | \([0, 0, 0, -20331, 1115802]\) | \(-11527859979/28\) | \(-2257403904\) | \([]\) | \(5184\) | \(1.0351\) | |
| 3024.bb2 | 3024o1 | \([0, 0, 0, -171, 2522]\) | \(-5000211/21952\) | \(-2427715584\) | \([]\) | \(1728\) | \(0.48579\) | \(\Gamma_0(N)\)-optimal |
| 3024.bb3 | 3024o2 | \([0, 0, 0, 1509, -60982]\) | \(381790581/1835008\) | \(-1826434842624\) | \([]\) | \(5184\) | \(1.0351\) |
Rank
sage: E.rank()
The elliptic curves in class 3024.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 3024.bb do not have complex multiplication.Modular form 3024.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
