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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 466752.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466752.z1 | 466752z2 | \([0, -1, 0, -40476671353, 3134417973989401]\) | \(1790515710161501896161423431416000/1239832650462893984887533\) | \(5078354536296013762099335168\) | \([2]\) | \(898007040\) | \(4.6304\) | \(\Gamma_0(N)\)-optimal* |
466752.z2 | 466752z1 | \([0, -1, 0, -2513818568, 49624889815314]\) | \(-27450200922351459504527329768000/736656099680135338407669537\) | \(-47145990379528661658090850368\) | \([2]\) | \(449003520\) | \(4.2839\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 466752.z have rank \(1\).
Complex multiplication
The elliptic curves in class 466752.z do not have complex multiplication.Modular form 466752.2.a.z
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 LMFDB 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 LMFDB labels.