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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 26520ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26520.r4 | 26520ba1 | \([0, 1, 0, -31, 52250]\) | \(-212629504/73740931875\) | \(-1179854910000\) | \([2]\) | \(51200\) | \(0.99525\) | \(\Gamma_0(N)\)-optimal |
| 26520.r3 | 26520ba2 | \([0, 1, 0, -21156, 1159200]\) | \(4090768940651344/72100305225\) | \(18457678137600\) | \([2, 2]\) | \(102400\) | \(1.3418\) | |
| 26520.r2 | 26520ba3 | \([0, 1, 0, -43256, -1704960]\) | \(8741236393854436/3852896763105\) | \(3945366285419520\) | \([2]\) | \(204800\) | \(1.6884\) | |
| 26520.r1 | 26520ba4 | \([0, 1, 0, -337056, 75206160]\) | \(4135530531909359236/1319214195\) | \(1350875335680\) | \([2]\) | \(204800\) | \(1.6884\) |
Rank
sage: E.rank()
The elliptic curves in class 26520ba have rank \(2\).
Complex multiplication
The elliptic curves in class 26520ba do not have complex multiplication.Modular form 26520.2.a.ba
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.
