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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 88305.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88305.k1 | 88305k4 | \([1, 1, 1, -94630, -11243098]\) | \(157551496201/13125\) | \(7807056088125\) | \([2]\) | \(401408\) | \(1.5177\) | |
| 88305.k2 | 88305k2 | \([1, 1, 1, -6325, -151990]\) | \(47045881/11025\) | \(6557927114025\) | \([2, 2]\) | \(200704\) | \(1.1711\) | |
| 88305.k3 | 88305k1 | \([1, 1, 1, -2120, 34712]\) | \(1771561/105\) | \(62456448705\) | \([2]\) | \(100352\) | \(0.82454\) | \(\Gamma_0(N)\)-optimal |
| 88305.k4 | 88305k3 | \([1, 1, 1, 14700, -925710]\) | \(590589719/972405\) | \(-578409171457005\) | \([2]\) | \(401408\) | \(1.5177\) |
Rank
sage: E.rank()
The elliptic curves in class 88305.k have rank \(1\).
Complex multiplication
The elliptic curves in class 88305.k do not have complex multiplication.Modular form 88305.2.a.k
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.
