Show commands:
SageMath
E = EllipticCurve("gz1")
E.isogeny_class()
Elliptic curves in class 92400gz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92400.hi2 | 92400gz1 | \([0, 1, 0, -3576133, -3049482637]\) | \(-79028701534867456/16987307596875\) | \(-1087187686200000000000\) | \([]\) | \(5760000\) | \(2.7576\) | \(\Gamma_0(N)\)-optimal |
92400.hi1 | 92400gz2 | \([0, 1, 0, -10716133, 255264377363]\) | \(-2126464142970105856/438611057788643355\) | \(-28071107698473174720000000\) | \([]\) | \(28800000\) | \(3.5624\) |
Rank
sage: E.rank()
The elliptic curves in class 92400gz have rank \(0\).
Complex multiplication
The elliptic curves in class 92400gz do not have complex multiplication.Modular form 92400.2.a.gz
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.