Show commands:
SageMath
E = EllipticCurve("nz1")
E.isogeny_class()
Elliptic curves in class 369600.nz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
369600.nz1 | 369600nz2 | \([0, 1, 0, -2073, -37017]\) | \(1925134784/693\) | \(354816000\) | \([2]\) | \(229376\) | \(0.60951\) | |
369600.nz2 | 369600nz1 | \([0, 1, 0, -148, -442]\) | \(45118016/17787\) | \(142296000\) | \([2]\) | \(114688\) | \(0.26293\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.nz have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.nz do not have complex multiplication.Modular form 369600.2.a.nz
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.