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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 9408.cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9408.cy1 | 9408bd3 | \([0, 1, 0, -29857, -1993153]\) | \(381775972/567\) | \(4371708837888\) | \([2]\) | \(24576\) | \(1.3265\) | |
| 9408.cy2 | 9408bd2 | \([0, 1, 0, -2417, -11985]\) | \(810448/441\) | \(850054496256\) | \([2, 2]\) | \(12288\) | \(0.97991\) | |
| 9408.cy3 | 9408bd1 | \([0, 1, 0, -1437, 20355]\) | \(2725888/21\) | \(2529924096\) | \([2]\) | \(6144\) | \(0.63334\) | \(\Gamma_0(N)\)-optimal |
| 9408.cy4 | 9408bd4 | \([0, 1, 0, 9343, -84897]\) | \(11696828/7203\) | \(-55536893755392\) | \([2]\) | \(24576\) | \(1.3265\) |
Rank
sage: E.rank()
The elliptic curves in class 9408.cy have rank \(1\).
Complex multiplication
The elliptic curves in class 9408.cy do not have complex multiplication.Modular form 9408.2.a.cy
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
