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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 296208r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296208.r2 | 296208r1 | \([0, 0, 0, 185856, -61311184]\) | \(134217728/384659\) | \(-2034789488589090816\) | \([]\) | \(4147200\) | \(2.1965\) | \(\Gamma_0(N)\)-optimal |
| 296208.r1 | 296208r2 | \([0, 0, 0, -1730784, 2004826736]\) | \(-108394872832/265513259\) | \(-1404526056830160777216\) | \([]\) | \(12441600\) | \(2.7458\) |
Rank
sage: E.rank()
The elliptic curves in class 296208r have rank \(0\).
Complex multiplication
The elliptic curves in class 296208r do not have complex multiplication.Modular form 296208.2.a.r
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
