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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 26026.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26026.e1 | 26026g4 | \([1, -1, 0, -872663, -313556619]\) | \(15226621995131793/2324168\) | \(11218315019912\) | \([2]\) | \(221184\) | \(1.9096\) | |
| 26026.e2 | 26026g3 | \([1, -1, 0, -102023, 4842085]\) | \(24331017010833/12004097336\) | \(57941485058280824\) | \([2]\) | \(221184\) | \(1.9096\) | |
| 26026.e3 | 26026g2 | \([1, -1, 0, -54703, -4858515]\) | \(3750606459153/45914176\) | \(221618957944384\) | \([2, 2]\) | \(110592\) | \(1.5631\) | |
| 26026.e4 | 26026g1 | \([1, -1, 0, -623, -196819]\) | \(-5545233/3469312\) | \(-16745706385408\) | \([2]\) | \(55296\) | \(1.2165\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26026.e have rank \(1\).
Complex multiplication
The elliptic curves in class 26026.e do not have complex multiplication.Modular form 26026.2.a.e
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
