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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 377520bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.bo4 | 377520bo1 | \([0, -1, 0, -558576, 265644480]\) | \(-2656166199049/2658140160\) | \(-19288299274198056960\) | \([2]\) | \(11059200\) | \(2.3962\) | \(\Gamma_0(N)\)-optimal |
| 377520.bo3 | 377520bo2 | \([0, -1, 0, -10470896, 13040642496]\) | \(17496824387403529/6580454400\) | \(47749842441496166400\) | \([2, 2]\) | \(22118400\) | \(2.7428\) | |
| 377520.bo1 | 377520bo3 | \([0, -1, 0, -167519216, 834591814080]\) | \(71647584155243142409/10140000\) | \(73579022499840000\) | \([2]\) | \(44236800\) | \(3.0894\) | |
| 377520.bo2 | 377520bo4 | \([0, -1, 0, -12019696, 8930746816]\) | \(26465989780414729/10571870144160\) | \(76712807810900925480960\) | \([2]\) | \(44236800\) | \(3.0894\) |
Rank
sage: E.rank()
The elliptic curves in class 377520bo have rank \(0\).
Complex multiplication
The elliptic curves in class 377520bo do not have complex multiplication.Modular form 377520.2.a.bo
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.
