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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 10010.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10010.s1 | 10010q2 | \([1, -1, 1, -170263, 26813281]\) | \(545861123494712462529/6289889684828750\) | \(6289889684828750\) | \([2]\) | \(69120\) | \(1.8443\) | |
10010.s2 | 10010q1 | \([1, -1, 1, -2193, 1064957]\) | \(-1165880220753249/488766923344700\) | \(-488766923344700\) | \([2]\) | \(34560\) | \(1.4977\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10010.s have rank \(0\).
Complex multiplication
The elliptic curves in class 10010.s do not have complex multiplication.Modular form 10010.2.a.s
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.