Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 57960.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57960.p1 | 57960bq4 | \([0, 0, 0, -73443, 7433102]\) | \(58687749106564/1988856345\) | \(1484673306117120\) | \([2]\) | \(425984\) | \(1.6834\) | |
| 57960.p2 | 57960bq2 | \([0, 0, 0, -11343, -304558]\) | \(864848456656/285779025\) | \(53333224761600\) | \([2, 2]\) | \(212992\) | \(1.3368\) | |
| 57960.p3 | 57960bq1 | \([0, 0, 0, -10218, -397483]\) | \(10115186538496/2113125\) | \(24647490000\) | \([2]\) | \(106496\) | \(0.99025\) | \(\Gamma_0(N)\)-optimal |
| 57960.p4 | 57960bq3 | \([0, 0, 0, 32757, -2095018]\) | \(5207251926236/5553444645\) | \(-4145624213713920\) | \([2]\) | \(425984\) | \(1.6834\) |
Rank
sage: E.rank()
The elliptic curves in class 57960.p have rank \(1\).
Complex multiplication
The elliptic curves in class 57960.p do not have complex multiplication.Modular form 57960.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
