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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 471510s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
471510.s2 | 471510s1 | \([1, -1, 0, -2649360, 1730540800]\) | \(-15780576012359283/787251200000\) | \(-102597601790361600000\) | \([2]\) | \(16588800\) | \(2.6009\) | \(\Gamma_0(N)\)-optimal* |
471510.s1 | 471510s2 | \([1, -1, 0, -42884880, 108105208576]\) | \(66928707375050045043/155000000000\) | \(20200195665000000000\) | \([2]\) | \(33177600\) | \(2.9474\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 471510s have rank \(0\).
Complex multiplication
The elliptic curves in class 471510s do not have complex multiplication.Modular form 471510.2.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.