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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 25872.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25872.g1 | 25872bo4 | \([0, -1, 0, -72131544, 235819764720]\) | \(86129359107301290313/9166294368\) | \(4417148379549007872\) | \([2]\) | \(2211840\) | \(3.0054\) | |
| 25872.g2 | 25872bo2 | \([0, -1, 0, -4519384, 3666652144]\) | \(21184262604460873/216872764416\) | \(104508882373746622464\) | \([2, 2]\) | \(1105920\) | \(2.6588\) | |
| 25872.g3 | 25872bo3 | \([0, -1, 0, -1132504, 9031470064]\) | \(-333345918055753/72923718045024\) | \(-35141232657526901047296\) | \([2]\) | \(2211840\) | \(3.0054\) | |
| 25872.g4 | 25872bo1 | \([0, -1, 0, -505304, -45569040]\) | \(29609739866953/15259926528\) | \(7353610633595584512\) | \([2]\) | \(552960\) | \(2.3123\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25872.g have rank \(1\).
Complex multiplication
The elliptic curves in class 25872.g do not have complex multiplication.Modular form 25872.2.a.g
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.
