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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 424830l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.l2 | 424830l1 | \([1, 1, 0, 1153827, -569065923]\) | \(59822347031/83966400\) | \(-238444495878866558400\) | \([2]\) | \(15925248\) | \(2.5957\) | \(\Gamma_0(N)\)-optimal* |
424830.l1 | 424830l2 | \([1, 1, 0, -7342773, -5644934763]\) | \(15417797707369/4080067320\) | \(11586415462247257516920\) | \([2]\) | \(31850496\) | \(2.9423\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 424830l have rank \(2\).
Complex multiplication
The elliptic curves in class 424830l do not have complex multiplication.Modular form 424830.2.a.l
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.