Show commands:
SageMath
E = EllipticCurve("hg1")
E.isogeny_class()
Elliptic curves in class 277200.hg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.hg1 | 277200hg1 | \([0, 0, 0, -13275, 588250]\) | \(598885164/539\) | \(232848000000\) | \([2]\) | \(458752\) | \(1.1055\) | \(\Gamma_0(N)\)-optimal |
277200.hg2 | 277200hg2 | \([0, 0, 0, -10275, 861250]\) | \(-138853062/290521\) | \(-251010144000000\) | \([2]\) | \(917504\) | \(1.4521\) |
Rank
sage: E.rank()
The elliptic curves in class 277200.hg have rank \(2\).
Complex multiplication
The elliptic curves in class 277200.hg do not have complex multiplication.Modular form 277200.2.a.hg
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.