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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 16224.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16224.d1 | 16224d1 | \([0, -1, 0, -490494, 132345108]\) | \(42246001231552/14414517\) | \(4452871704720192\) | \([2]\) | \(129024\) | \(1.9743\) | \(\Gamma_0(N)\)-optimal |
| 16224.d2 | 16224d2 | \([0, -1, 0, -422049, 170523729]\) | \(-420526439488/390971529\) | \(-7729745489596256256\) | \([2]\) | \(258048\) | \(2.3208\) |
Rank
sage: E.rank()
The elliptic curves in class 16224.d have rank \(1\).
Complex multiplication
The elliptic curves in class 16224.d do not have complex multiplication.Modular form 16224.2.a.d
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.
