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SageMath
E = EllipticCurve("iy1")
E.isogeny_class()
Elliptic curves in class 479808iy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
479808.iy2 | 479808iy1 | \([0, 0, 0, -508620, -138994576]\) | \(647214625/3332\) | \(74913602646048768\) | \([2]\) | \(3538944\) | \(2.0838\) | \(\Gamma_0(N)\)-optimal* |
479808.iy1 | 479808iy2 | \([0, 0, 0, -790860, 32494448]\) | \(2433138625/1387778\) | \(31201515502079311872\) | \([2]\) | \(7077888\) | \(2.4304\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 479808iy have rank \(1\).
Complex multiplication
The elliptic curves in class 479808iy do not have complex multiplication.Modular form 479808.2.a.iy
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.