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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 23534.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23534.w1 | 23534u2 | \([1, -1, 1, -16156616628, -790444758984737]\) | \(98191033604529537629349729/10906239337336\) | \(51805773729640763241976\) | \([]\) | \(41489280\) | \(4.2275\) | |
23534.w2 | 23534u1 | \([1, -1, 1, -32531868, 65750158303]\) | \(801581275315909089/70810888830976\) | \(336359103344998629769216\) | \([]\) | \(5927040\) | \(3.2546\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23534.w have rank \(0\).
Complex multiplication
The elliptic curves in class 23534.w do not have complex multiplication.Modular form 23534.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.