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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 176176.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176176.bo1 | 176176ba4 | \([0, 0, 0, -19196771, -32373553630]\) | \(107818231938348177/4463459\) | \(32388259387387904\) | \([2]\) | \(4669440\) | \(2.6543\) | |
| 176176.bo2 | 176176ba3 | \([0, 0, 0, -1947011, 195995074]\) | \(112489728522417/62811265517\) | \(455778256283902103552\) | \([4]\) | \(4669440\) | \(2.6543\) | |
| 176176.bo3 | 176176ba2 | \([0, 0, 0, -1201651, -504196110]\) | \(26444947540257/169338169\) | \(1228770902064369664\) | \([2, 2]\) | \(2334720\) | \(2.3078\) | |
| 176176.bo4 | 176176ba1 | \([0, 0, 0, -30371, -17177886]\) | \(-426957777/17320303\) | \(-125681554649018368\) | \([2]\) | \(1167360\) | \(1.9612\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176176.bo have rank \(2\).
Complex multiplication
The elliptic curves in class 176176.bo do not have complex multiplication.Modular form 176176.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
