Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 6384.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6384.k1 | 6384e2 | \([0, -1, 0, -168, 864]\) | \(515150500/22743\) | \(23288832\) | \([2]\) | \(1536\) | \(0.17662\) | |
6384.k2 | 6384e1 | \([0, -1, 0, -28, -32]\) | \(9826000/2793\) | \(715008\) | \([2]\) | \(768\) | \(-0.16995\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6384.k have rank \(1\).
Complex multiplication
The elliptic curves in class 6384.k do not have complex multiplication.Modular form 6384.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.