Show commands:
SageMath
E = EllipticCurve("dz1")
E.isogeny_class()
Elliptic curves in class 9450.dz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9450.dz1 | 9450da1 | \([1, -1, 1, -305, -2053]\) | \(-296595/14\) | \(-147656250\) | \([]\) | \(5400\) | \(0.33038\) | \(\Gamma_0(N)\)-optimal |
9450.dz2 | 9450da2 | \([1, -1, 1, 1570, -5803]\) | \(4511445/2744\) | \(-260465625000\) | \([3]\) | \(16200\) | \(0.87969\) |
Rank
sage: E.rank()
The elliptic curves in class 9450.dz have rank \(0\).
Complex multiplication
The elliptic curves in class 9450.dz do not have complex multiplication.Modular form 9450.2.a.dz
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.