Show commands:
SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 9360.ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9360.ca1 | 9360bx1 | \([0, 0, 0, -147, 146]\) | \(117649/65\) | \(194088960\) | \([2]\) | \(3072\) | \(0.28084\) | \(\Gamma_0(N)\)-optimal |
9360.ca2 | 9360bx2 | \([0, 0, 0, 573, 1154]\) | \(6967871/4225\) | \(-12615782400\) | \([2]\) | \(6144\) | \(0.62741\) |
Rank
sage: E.rank()
The elliptic curves in class 9360.ca have rank \(0\).
Complex multiplication
The elliptic curves in class 9360.ca do not have complex multiplication.Modular form 9360.2.a.ca
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.