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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 180999s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
180999.q1 | 180999s1 | \([1, -1, 0, -71196774, -231179291641]\) | \(420100556152674123/62939003491\) | \(5979588098152863680577\) | \([2]\) | \(23224320\) | \(3.1918\) | \(\Gamma_0(N)\)-optimal |
180999.q2 | 180999s2 | \([1, -1, 0, -64603239, -275731807636]\) | \(-313859434290315003/164114213839849\) | \(-15591848383090490092166403\) | \([2]\) | \(46448640\) | \(3.5384\) |
Rank
sage: E.rank()
The elliptic curves in class 180999s have rank \(1\).
Complex multiplication
The elliptic curves in class 180999s do not have complex multiplication.Modular form 180999.2.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 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.