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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 262080.db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 262080.db1 | 262080db4 | \([0, 0, 0, -48672588, -130699754512]\) | \(266912903848829942596/152163375\) | \(7269718450176000\) | \([2]\) | \(11010048\) | \(2.8045\) | |
| 262080.db2 | 262080db2 | \([0, 0, 0, -3042588, -2041406512]\) | \(260798860029250384/196803140625\) | \(2350604116224000000\) | \([2, 2]\) | \(5505024\) | \(2.4579\) | |
| 262080.db3 | 262080db3 | \([0, 0, 0, -2412588, -2911058512]\) | \(-32506165579682596/57814914850875\) | \(-2762150571297202176000\) | \([2]\) | \(11010048\) | \(2.8045\) | |
| 262080.db4 | 262080db1 | \([0, 0, 0, -230088, -17531512]\) | \(1804588288006144/866455078125\) | \(646805250000000000\) | \([2]\) | \(2752512\) | \(2.1113\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 262080.db have rank \(1\).
Complex multiplication
The elliptic curves in class 262080.db do not have complex multiplication.Modular form 262080.2.a.db
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.
