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SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 139650.em
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139650.em1 | 139650dq2 | \([1, 1, 1, -1982688, -1075372719]\) | \(468898230633769/5540400\) | \(10184726868750000\) | \([2]\) | \(3317760\) | \(2.2217\) | |
139650.em2 | 139650dq1 | \([1, 1, 1, -120688, -17756719]\) | \(-105756712489/12476160\) | \(-22934496060000000\) | \([2]\) | \(1658880\) | \(1.8751\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 139650.em have rank \(0\).
Complex multiplication
The elliptic curves in class 139650.em do not have complex multiplication.Modular form 139650.2.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.