Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 9450.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9450.y1 | 9450bf1 | \([1, -1, 0, -12, -14]\) | \(-296595/14\) | \(-9450\) | \([]\) | \(1080\) | \(-0.47434\) | \(\Gamma_0(N)\)-optimal |
9450.y2 | 9450bf2 | \([1, -1, 0, 63, -59]\) | \(4511445/2744\) | \(-16669800\) | \([]\) | \(3240\) | \(0.074970\) |
Rank
sage: E.rank()
The elliptic curves in class 9450.y have rank \(0\).
Complex multiplication
The elliptic curves in class 9450.y do not have complex multiplication.Modular form 9450.2.a.y
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.