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SageMath
sage: E = EllipticCurve("wz1")
sage: E.isogeny_class()
Elliptic curves in class 369600.wz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.wz1 | 369600wz2 | \([0, 1, 0, -3626257313, -22549816971297]\) | \(160934676078320454012702173/86430430219822569086976\) | \(2832152337443145943842029568000\) | \([2]\) | \(644087808\) | \(4.5344\) | |
| 369600.wz2 | 369600wz1 | \([0, 1, 0, 869512287, -2763934961697]\) | \(2218712073897830722499107/1384711926834951880704\) | \(-45374240418527703226908672000\) | \([2]\) | \(322043904\) | \(4.1878\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.wz have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.wz do not have complex multiplication.Modular form 369600.2.a.wz
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.
