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SageMath
E = EllipticCurve("iw1")
E.isogeny_class()
Elliptic curves in class 193600iw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193600.hv2 | 193600iw1 | \([0, -1, 0, -1552833, -384486463]\) | \(18865/8\) | \(175602795315200000000\) | \([]\) | \(6082560\) | \(2.5813\) | \(\Gamma_0(N)\)-optimal |
| 193600.hv1 | 193600iw2 | \([0, -1, 0, -108032833, -432160886463]\) | \(6352571665/2\) | \(43900698828800000000\) | \([]\) | \(18247680\) | \(3.1306\) |
Rank
sage: E.rank()
The elliptic curves in class 193600iw have rank \(1\).
Complex multiplication
The elliptic curves in class 193600iw do not have complex multiplication.Modular form 193600.2.a.iw
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
