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SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 479808.em
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
479808.em1 | 479808em2 | \([0, 0, 0, -10288236, -288048656]\) | \(42852953779784/24786408969\) | \(69659333453110943711232\) | \([2]\) | \(35389440\) | \(3.0726\) | \(\Gamma_0(N)\)-optimal* |
479808.em2 | 479808em1 | \([0, 0, 0, 2571324, -36001280]\) | \(5352028359488/3098832471\) | \(-1088613747370045403136\) | \([2]\) | \(17694720\) | \(2.7261\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 479808.em have rank \(1\).
Complex multiplication
The elliptic curves in class 479808.em do not have complex multiplication.Modular form 479808.2.a.em
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.