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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 206310bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206310.ba4 | 206310bo1 | \([1, 0, 1, -152628, -37928654]\) | \(-2656166199049/2658140160\) | \(-393500141672202240\) | \([2]\) | \(3604480\) | \(2.0719\) | \(\Gamma_0(N)\)-optimal |
| 206310.ba3 | 206310bo2 | \([1, 0, 1, -2861108, -1862360782]\) | \(17496824387403529/6580454400\) | \(974143417127961600\) | \([2, 2]\) | \(7208960\) | \(2.4184\) | |
| 206310.ba2 | 206310bo3 | \([1, 0, 1, -3284308, -1275297742]\) | \(26465989780414729/10571870144160\) | \(1565016195183283758240\) | \([2]\) | \(14417920\) | \(2.7650\) | |
| 206310.ba1 | 206310bo4 | \([1, 0, 1, -45773588, -119202246094]\) | \(71647584155243142409/10140000\) | \(1501083914460000\) | \([2]\) | \(14417920\) | \(2.7650\) |
Rank
sage: E.rank()
The elliptic curves in class 206310bo have rank \(0\).
Complex multiplication
The elliptic curves in class 206310bo do not have complex multiplication.Modular form 206310.2.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.
