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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 161700cs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
161700.g1 | 161700cs1 | \([0, -1, 0, -1754853, -894084498]\) | \(2539966281285632/316377369\) | \(74442962170962000\) | \([2]\) | \(2506752\) | \(2.2602\) | \(\Gamma_0(N)\)-optimal |
161700.g2 | 161700cs2 | \([0, -1, 0, -1606628, -1051499448]\) | \(-121823692387472/56500814601\) | \(-212712458783777568000\) | \([2]\) | \(5013504\) | \(2.6068\) |
Rank
sage: E.rank()
The elliptic curves in class 161700cs have rank \(0\).
Complex multiplication
The elliptic curves in class 161700cs do not have complex multiplication.Modular form 161700.2.a.cs
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.