Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 184041.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
184041.k1 | 184041j2 | \([1, -1, 1, -463937, -475341798]\) | \(-121\) | \(-91267150991176664361\) | \([]\) | \(3706560\) | \(2.5128\) | |
184041.k2 | 184041j1 | \([1, -1, 1, -45662, 3767118]\) | \(-24729001\) | \(-425767995081\) | \([]\) | \(336960\) | \(1.3138\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 184041.k have rank \(1\).
Complex multiplication
The elliptic curves in class 184041.k do not have complex multiplication.Modular form 184041.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.