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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 54390bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54390.x4 | 54390bb1 | \([1, 0, 1, 315387, -192592592]\) | \(29489595518609351/153302146744320\) | \(-18035844262322503680\) | \([2]\) | \(1548288\) | \(2.3771\) | \(\Gamma_0(N)\)-optimal |
| 54390.x3 | 54390bb2 | \([1, 0, 1, -3698693, -2458139344]\) | \(47564195924660918329/5343633392025600\) | \(628673124938419814400\) | \([2, 2]\) | \(3096576\) | \(2.7236\) | |
| 54390.x2 | 54390bb3 | \([1, 0, 1, -14141573, 17846996528]\) | \(2658450554295301169209/368731891034640000\) | \(43380938248334361360000\) | \([2]\) | \(6193152\) | \(3.0702\) | |
| 54390.x1 | 54390bb4 | \([1, 0, 1, -57481093, -167742211024]\) | \(178529715976079010844729/2699299212865920\) | \(317569853094462622080\) | \([2]\) | \(6193152\) | \(3.0702\) |
Rank
sage: E.rank()
The elliptic curves in class 54390bb have rank \(0\).
Complex multiplication
The elliptic curves in class 54390bb do not have complex multiplication.Modular form 54390.2.a.bb
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.
