Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 450528.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450528.q1 | 450528q2 | \([0, -1, 0, -12033, -174831]\) | \(1000000/507\) | \(97698863788032\) | \([2]\) | \(912384\) | \(1.3769\) | |
450528.q2 | 450528q1 | \([0, -1, 0, -6618, 207468]\) | \(10648000/117\) | \(352279556928\) | \([2]\) | \(456192\) | \(1.0303\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 450528.q have rank \(0\).
Complex multiplication
The elliptic curves in class 450528.q do not have complex multiplication.Modular form 450528.2.a.q
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.