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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 49725s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49725.g2 | 49725s1 | \([1, -1, 1, -164855, -25679978]\) | \(43499078731809/82055753\) | \(934666311515625\) | \([2]\) | \(307200\) | \(1.7626\) | \(\Gamma_0(N)\)-optimal |
49725.g1 | 49725s2 | \([1, -1, 1, -2636480, -1647065978]\) | \(177930109857804849/634933\) | \(7232283703125\) | \([2]\) | \(614400\) | \(2.1092\) |
Rank
sage: E.rank()
The elliptic curves in class 49725s have rank \(0\).
Complex multiplication
The elliptic curves in class 49725s do not have complex multiplication.Modular form 49725.2.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.