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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 62790.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62790.f1 | 62790f4 | \([1, 1, 0, -31902, 2179944]\) | \(3590861998743389161/1162996380\) | \(1162996380\) | \([2]\) | \(139264\) | \(1.0994\) | |
| 62790.f2 | 62790f3 | \([1, 1, 0, -4102, -51296]\) | \(7636178954937961/3356866296420\) | \(3356866296420\) | \([2]\) | \(139264\) | \(1.0994\) | |
| 62790.f3 | 62790f2 | \([1, 1, 0, -2002, 33124]\) | \(888085626379561/15770336400\) | \(15770336400\) | \([2, 2]\) | \(69632\) | \(0.75278\) | |
| 62790.f4 | 62790f1 | \([1, 1, 0, -2, 1524]\) | \(-1771561/1004640000\) | \(-1004640000\) | \([2]\) | \(34816\) | \(0.40621\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62790.f have rank \(1\).
Complex multiplication
The elliptic curves in class 62790.f do not have complex multiplication.Modular form 62790.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
