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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 16562.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16562.v1 | 16562p1 | \([1, 1, 0, -33296, -2352748]\) | \(-1214950633/196\) | \(-658593925444\) | \([]\) | \(69120\) | \(1.2773\) | \(\Gamma_0(N)\)-optimal |
16562.v2 | 16562p2 | \([1, 1, 0, 8109, -7644307]\) | \(17546087/7529536\) | \(-25300544239856704\) | \([]\) | \(207360\) | \(1.8266\) |
Rank
sage: E.rank()
The elliptic curves in class 16562.v have rank \(0\).
Complex multiplication
The elliptic curves in class 16562.v do not have complex multiplication.Modular form 16562.2.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 LMFDB 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 LMFDB labels.