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SageMath
E = EllipticCurve("eg1")
E.isogeny_class()
Elliptic curves in class 65520.eg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 65520.eg1 | 65520bl4 | \([0, 0, 0, -12168147, 16337469314]\) | \(266912903848829942596/152163375\) | \(113589350784000\) | \([4]\) | \(1376256\) | \(2.4579\) | |
| 65520.eg2 | 65520bl2 | \([0, 0, 0, -760647, 255175814]\) | \(260798860029250384/196803140625\) | \(36728189316000000\) | \([2, 2]\) | \(688128\) | \(2.1113\) | |
| 65520.eg3 | 65520bl3 | \([0, 0, 0, -603147, 363882314]\) | \(-32506165579682596/57814914850875\) | \(-43158602676518784000\) | \([2]\) | \(1376256\) | \(2.4579\) | |
| 65520.eg4 | 65520bl1 | \([0, 0, 0, -57522, 2191439]\) | \(1804588288006144/866455078125\) | \(10106332031250000\) | \([2]\) | \(344064\) | \(1.7648\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 65520.eg have rank \(0\).
Complex multiplication
The elliptic curves in class 65520.eg do not have complex multiplication.Modular form 65520.2.a.eg
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.
