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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 429429w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
429429.w2 | 429429w1 | \([1, 1, 1, -176602, 30273134]\) | \(-156503678869/11647251\) | \(-45332492936497767\) | \([2]\) | \(3732480\) | \(1.9448\) | \(\Gamma_0(N)\)-optimal* |
429429.w1 | 429429w2 | \([1, 1, 1, -2874297, 1874417436]\) | \(674733819141829/3361743\) | \(13084305541438131\) | \([2]\) | \(7464960\) | \(2.2914\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 429429w have rank \(1\).
Complex multiplication
The elliptic curves in class 429429w do not have complex multiplication.Modular form 429429.2.a.w
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.