Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 91200.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
91200.p1 | 91200o1 | \([0, -1, 0, -1633, 23137]\) | \(470596/57\) | \(58368000000\) | \([2]\) | \(102400\) | \(0.79637\) | \(\Gamma_0(N)\)-optimal |
91200.p2 | 91200o2 | \([0, -1, 0, 2367, 115137]\) | \(715822/3249\) | \(-6653952000000\) | \([2]\) | \(204800\) | \(1.1429\) |
Rank
sage: E.rank()
The elliptic curves in class 91200.p have rank \(1\).
Complex multiplication
The elliptic curves in class 91200.p do not have complex multiplication.Modular form 91200.2.a.p
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.