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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 161700.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 161700.z1 | 161700ef2 | \([0, -1, 0, -43458508, 89343065512]\) | \(19288565375865424/3837216796875\) | \(1805778875742187500000000\) | \([2]\) | \(19906560\) | \(3.3707\) | |
| 161700.z2 | 161700ef1 | \([0, -1, 0, 5657867, 8301046762]\) | \(681010157060096/1406657896875\) | \(-41372973727361718750000\) | \([2]\) | \(9953280\) | \(3.0241\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 161700.z have rank \(1\).
Complex multiplication
The elliptic curves in class 161700.z do not have complex multiplication.Modular form 161700.2.a.z
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.
