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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 152592de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152592.n3 | 152592de1 | \([0, -1, 0, -3564, 80160]\) | \(810448/33\) | \(203914182912\) | \([2]\) | \(147456\) | \(0.93587\) | \(\Gamma_0(N)\)-optimal |
| 152592.n2 | 152592de2 | \([0, -1, 0, -9344, -238896]\) | \(3650692/1089\) | \(26916672144384\) | \([2, 2]\) | \(294912\) | \(1.2824\) | |
| 152592.n4 | 152592de3 | \([0, -1, 0, 25336, -1626096]\) | \(36382894/43923\) | \(-2171278219646976\) | \([2]\) | \(589824\) | \(1.6290\) | |
| 152592.n1 | 152592de4 | \([0, -1, 0, -136504, -19363760]\) | \(5690357426/891\) | \(44045463508992\) | \([2]\) | \(589824\) | \(1.6290\) |
Rank
sage: E.rank()
The elliptic curves in class 152592de have rank \(0\).
Complex multiplication
The elliptic curves in class 152592de do not have complex multiplication.Modular form 152592.2.a.de
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 Cremona 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 Cremona labels.
