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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 435344x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435344.x2 | 435344x1 | \([0, 0, 0, -9971, -435006]\) | \(-22180932/3703\) | \(-18302641896448\) | \([2]\) | \(552960\) | \(1.2718\) | \(\Gamma_0(N)\)-optimal* |
435344.x1 | 435344x2 | \([0, 0, 0, -165451, -25902630]\) | \(50668941906/1127\) | \(11140738545664\) | \([2]\) | \(1105920\) | \(1.6184\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435344x have rank \(0\).
Complex multiplication
The elliptic curves in class 435344x do not have complex multiplication.Modular form 435344.2.a.x
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.