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SageMath
sage: E = EllipticCurve("9900.bd1")
sage: E.isogeny_class()
Elliptic curves in class 9900.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 9900.bd1 | 9900t4 | [0, 0, 0, -1597575, 777212750] | [2] | 124416 | |
| 9900.bd2 | 9900t3 | [0, 0, 0, -100200, 12054125] | [2] | 62208 | |
| 9900.bd3 | 9900t2 | [0, 0, 0, -22575, 737750] | [2] | 41472 | |
| 9900.bd4 | 9900t1 | [0, 0, 0, -10200, -388375] | [2] | 20736 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9900.bd have rank \(0\).
Modular form 9900.2.a.bd
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
