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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 8624.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8624.r1 | 8624x2 | \([0, 0, 0, -367843, 85870050]\) | \(11422548526761/4312\) | \(2077910990848\) | \([2]\) | \(55296\) | \(1.7141\) | |
| 8624.r2 | 8624x1 | \([0, 0, 0, -22883, 1354850]\) | \(-2749884201/54208\) | \(-26122309599232\) | \([2]\) | \(27648\) | \(1.3675\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8624.r have rank \(0\).
Complex multiplication
The elliptic curves in class 8624.r do not have complex multiplication.Modular form 8624.2.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 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.
