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SageMath
E = EllipticCurve("ii1")
E.isogeny_class()
Elliptic curves in class 179520.ii
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179520.ii1 | 179520fo1 | \([0, 1, 0, -5665, -140737]\) | \(76711450249/12622500\) | \(3308912640000\) | \([2]\) | \(368640\) | \(1.1239\) | \(\Gamma_0(N)\)-optimal |
| 179520.ii2 | 179520fo2 | \([0, 1, 0, 10335, -777537]\) | \(465664585751/1274620050\) | \(-334133998387200\) | \([2]\) | \(737280\) | \(1.4705\) |
Rank
sage: E.rank()
The elliptic curves in class 179520.ii have rank \(0\).
Complex multiplication
The elliptic curves in class 179520.ii do not have complex multiplication.Modular form 179520.2.a.ii
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.
