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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 110946.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 110946.bo1 | 110946bm4 | \([1, 0, 0, -591747, -175256625]\) | \(4824238966273/66\) | \(313506879906\) | \([2]\) | \(1105920\) | \(1.7618\) | |
| 110946.bo2 | 110946bm2 | \([1, 0, 0, -37017, -2735595]\) | \(1180932193/4356\) | \(20691454073796\) | \([2, 2]\) | \(552960\) | \(1.4153\) | |
| 110946.bo3 | 110946bm3 | \([1, 0, 0, -20207, -5226837]\) | \(-192100033/2371842\) | \(-11266496743181922\) | \([2]\) | \(1105920\) | \(1.7618\) | |
| 110946.bo4 | 110946bm1 | \([1, 0, 0, -3397, 1073]\) | \(912673/528\) | \(2508055039248\) | \([2]\) | \(276480\) | \(1.0687\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 110946.bo have rank \(0\).
Complex multiplication
The elliptic curves in class 110946.bo do not have complex multiplication.Modular form 110946.2.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 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.
