Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 136458.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 136458.n1 | 136458ca3 | \([1, -1, 0, -3451047, 2468461103]\) | \(-545407363875/14\) | \(-116676513541098\) | \([]\) | \(2309472\) | \(2.2154\) | |
| 136458.n2 | 136458ca2 | \([1, -1, 0, -39597, 3893165]\) | \(-7414875/2744\) | \(-2540955183783912\) | \([]\) | \(769824\) | \(1.6661\) | |
| 136458.n3 | 136458ca1 | \([1, -1, 0, 3723, -54731]\) | \(4492125/3584\) | \(-4552535812608\) | \([]\) | \(256608\) | \(1.1168\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 136458.n have rank \(1\).
Complex multiplication
The elliptic curves in class 136458.n do not have complex multiplication.Modular form 136458.2.a.n
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
