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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 51600.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51600.w1 | 51600bo1 | \([0, -1, 0, -61811008, 186593984512]\) | \(408076159454905367161/1190206406250000\) | \(76173210000000000000000\) | \([2]\) | \(6082560\) | \(3.2611\) | \(\Gamma_0(N)\)-optimal |
| 51600.w2 | 51600bo2 | \([0, -1, 0, -36811008, 338893984512]\) | \(-86193969101536367161/725294740213012500\) | \(-46418863373632800000000000\) | \([2]\) | \(12165120\) | \(3.6077\) |
Rank
sage: E.rank()
The elliptic curves in class 51600.w have rank \(0\).
Complex multiplication
The elliptic curves in class 51600.w do not have complex multiplication.Modular form 51600.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
