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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 162450v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162450.dd2 | 162450v1 | \([1, -1, 1, -50855, 4557647]\) | \(-186169411/6480\) | \(-506271363750000\) | \([2]\) | \(737280\) | \(1.5945\) | \(\Gamma_0(N)\)-optimal |
| 162450.dd1 | 162450v2 | \([1, -1, 1, -820355, 286194647]\) | \(781484460931/900\) | \(70315467187500\) | \([2]\) | \(1474560\) | \(1.9410\) |
Rank
sage: E.rank()
The elliptic curves in class 162450v have rank \(1\).
Complex multiplication
The elliptic curves in class 162450v do not have complex multiplication.Modular form 162450.2.a.v
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.
