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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 18496r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18496.d2 | 18496r1 | \([0, 1, 0, -9633, 261727]\) | \(62500/17\) | \(26891955273728\) | \([2]\) | \(36864\) | \(1.2848\) | \(\Gamma_0(N)\)-optimal |
| 18496.d1 | 18496r2 | \([0, 1, 0, -55873, -4889409]\) | \(6097250/289\) | \(914326479306752\) | \([2]\) | \(73728\) | \(1.6313\) |
Rank
sage: E.rank()
The elliptic curves in class 18496r have rank \(0\).
Complex multiplication
The elliptic curves in class 18496r do not have complex multiplication.Modular form 18496.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
