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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 424830u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.u2 | 424830u1 | \([1, 1, 0, 6659443612, -2754863188541232]\) | \(11501534367688741509671/1161179873437500000000\) | \(-3297473150527958333498437500000000\) | \([2]\) | \(2972712960\) | \(5.1110\) | \(\Gamma_0(N)\)-optimal* |
424830.u1 | 424830u2 | \([1, 1, 0, -258859306388, -49006795637291232]\) | \(675512349748162449958490329/25568496800736303750000\) | \(72608416343108438167646607603750000\) | \([2]\) | \(5945425920\) | \(5.4575\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 424830u have rank \(0\).
Complex multiplication
The elliptic curves in class 424830u do not have complex multiplication.Modular form 424830.2.a.u
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.