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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 330096de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 330096.de3 | 330096de1 | \([0, 1, 0, -20807, 1148028]\) | \(420616192/117\) | \(277123184208\) | \([2]\) | \(720896\) | \(1.1774\) | \(\Gamma_0(N)\)-optimal |
| 330096.de2 | 330096de2 | \([0, 1, 0, -23452, 834860]\) | \(37642192/13689\) | \(518774600837376\) | \([2, 2]\) | \(1441792\) | \(1.5240\) | |
| 330096.de4 | 330096de3 | \([0, 1, 0, 71768, 5976740]\) | \(269676572/257049\) | \(-38965736685118464\) | \([2]\) | \(2883584\) | \(1.8706\) | |
| 330096.de1 | 330096de4 | \([0, 1, 0, -160992, -24307452]\) | \(3044193988/85293\) | \(12929459282408448\) | \([2]\) | \(2883584\) | \(1.8706\) |
Rank
sage: E.rank()
The elliptic curves in class 330096de have rank \(0\).
Complex multiplication
The elliptic curves in class 330096de do not have complex multiplication.Modular form 330096.2.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.
