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SageMath
E = EllipticCurve("ii1")
E.isogeny_class()
Elliptic curves in class 485100.ii
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 485100.ii1 | 485100ii1 | \([0, 0, 0, -6825, 219625]\) | \(-3937024/55\) | \(-491163750000\) | \([]\) | \(746496\) | \(1.0493\) | \(\Gamma_0(N)\)-optimal |
| 485100.ii2 | 485100ii2 | \([0, 0, 0, 24675, 1101625]\) | \(186050816/166375\) | \(-1485770343750000\) | \([]\) | \(2239488\) | \(1.5986\) |
Rank
sage: E.rank()
The elliptic curves in class 485100.ii have rank \(1\).
Complex multiplication
The elliptic curves in class 485100.ii do not have complex multiplication.Modular form 485100.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
