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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 156816f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 156816.bt4 | 156816f1 | \([0, 0, 0, 5445, -23958]\) | \(3375/2\) | \(-10579705602048\) | \([]\) | \(194400\) | \(1.1885\) | \(\Gamma_0(N)\)-optimal |
| 156816.bt3 | 156816f2 | \([0, 0, 0, -81675, -9415494]\) | \(-140625/8\) | \(-3427824615063552\) | \([]\) | \(583200\) | \(1.7378\) | |
| 156816.bt1 | 156816f3 | \([0, 0, 0, -2085435, 1159159914]\) | \(-189613868625/128\) | \(-677101158531072\) | \([]\) | \(1360800\) | \(2.1615\) | |
| 156816.bt2 | 156816f4 | \([0, 0, 0, -1649835, 1656911322]\) | \(-1159088625/2097152\) | \(-898583655891219775488\) | \([]\) | \(4082400\) | \(2.7108\) |
Rank
sage: E.rank()
The elliptic curves in class 156816f have rank \(0\).
Complex multiplication
The elliptic curves in class 156816f do not have complex multiplication.Modular form 156816.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
