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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 162450.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162450.x1 | 162450es2 | \([1, -1, 0, -21959517, -39602421859]\) | \(8602523649/8\) | \(1089070980004125000\) | \([2]\) | \(9338880\) | \(2.7577\) | |
| 162450.x2 | 162450es1 | \([1, -1, 0, -1382517, -609006859]\) | \(2146689/64\) | \(8712567840033000000\) | \([2]\) | \(4669440\) | \(2.4111\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162450.x have rank \(1\).
Complex multiplication
The elliptic curves in class 162450.x do not have complex multiplication.Modular form 162450.2.a.x
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.
