Show commands:
SageMath
E = EllipticCurve("gz1")
E.isogeny_class()
Elliptic curves in class 193200.gz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193200.gz1 | 193200bm1 | \([0, 1, 0, -9408, -196812]\) | \(1439069689/579600\) | \(37094400000000\) | \([2]\) | \(442368\) | \(1.3017\) | \(\Gamma_0(N)\)-optimal |
193200.gz2 | 193200bm2 | \([0, 1, 0, 30592, -1396812]\) | \(49471280711/41992020\) | \(-2687489280000000\) | \([2]\) | \(884736\) | \(1.6482\) |
Rank
sage: E.rank()
The elliptic curves in class 193200.gz have rank \(0\).
Complex multiplication
The elliptic curves in class 193200.gz do not have complex multiplication.Modular form 193200.2.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 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.