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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 481338z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
481338.z2 | 481338z1 | \([1, -1, 0, -22347, 650997]\) | \(955671625/413712\) | \(534295796390928\) | \([2]\) | \(1433600\) | \(1.5222\) | \(\Gamma_0(N)\)-optimal* |
481338.z1 | 481338z2 | \([1, -1, 0, -305487, 65037033]\) | \(2441288319625/1217268\) | \(1572062631688692\) | \([2]\) | \(2867200\) | \(1.8688\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 481338z have rank \(1\).
Complex multiplication
The elliptic curves in class 481338z do not have complex multiplication.Modular form 481338.2.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 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.