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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 199920.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 199920.f1 | 199920da3 | \([0, -1, 0, -795776, 211116480]\) | \(115650783909361/27072079335\) | \(13045772540655267840\) | \([2]\) | \(4718592\) | \(2.3797\) | |
| 199920.f2 | 199920da2 | \([0, -1, 0, -266576, -50096640]\) | \(4347507044161/258084225\) | \(124368285642854400\) | \([2, 2]\) | \(2359296\) | \(2.0332\) | |
| 199920.f3 | 199920da1 | \([0, -1, 0, -262656, -51724224]\) | \(4158523459441/16065\) | \(7741567733760\) | \([2]\) | \(1179648\) | \(1.6866\) | \(\Gamma_0(N)\)-optimal |
| 199920.f4 | 199920da4 | \([0, -1, 0, 199904, -207207104]\) | \(1833318007919/39525924375\) | \(-19047159712949760000\) | \([2]\) | \(4718592\) | \(2.3797\) |
Rank
sage: E.rank()
The elliptic curves in class 199920.f have rank \(1\).
Complex multiplication
The elliptic curves in class 199920.f do not have complex multiplication.Modular form 199920.2.a.f
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.
