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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 17160.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17160.p1 | 17160f3 | \([0, 1, 0, -15256, 720224]\) | \(383507853966436/57915\) | \(59304960\) | \([2]\) | \(20480\) | \(0.89777\) | |
| 17160.p2 | 17160f2 | \([0, 1, 0, -956, 10944]\) | \(377843214544/4601025\) | \(1177862400\) | \([2, 2]\) | \(10240\) | \(0.55120\) | |
| 17160.p3 | 17160f4 | \([0, 1, 0, -176, 29040]\) | \(-592143556/356874375\) | \(-365439360000\) | \([2]\) | \(20480\) | \(0.89777\) | |
| 17160.p4 | 17160f1 | \([0, 1, 0, -111, -210]\) | \(9538484224/4712565\) | \(75401040\) | \([2]\) | \(5120\) | \(0.20463\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17160.p have rank \(0\).
Complex multiplication
The elliptic curves in class 17160.p do not have complex multiplication.Modular form 17160.2.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.
