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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 323400.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 323400.w1 | 323400w2 | \([0, -1, 0, -449248, -5689508]\) | \(665863066004/384359283\) | \(5788094116565376000\) | \([2]\) | \(6193152\) | \(2.2897\) | |
| 323400.w2 | 323400w1 | \([0, -1, 0, -316948, -68399708]\) | \(935299949456/2750517\) | \(10355058385056000\) | \([2]\) | \(3096576\) | \(1.9431\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 323400.w have rank \(0\).
Complex multiplication
The elliptic curves in class 323400.w do not have complex multiplication.Modular form 323400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
