Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 100800.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.a1 | 100800hj2 | \([0, 0, 0, -124500, -16900000]\) | \(36594368/21\) | \(122472000000000\) | \([2]\) | \(655360\) | \(1.6493\) | |
100800.a2 | 100800hj1 | \([0, 0, 0, -6375, -362500]\) | \(-314432/441\) | \(-40186125000000\) | \([2]\) | \(327680\) | \(1.3027\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100800.a have rank \(1\).
Complex multiplication
The elliptic curves in class 100800.a do not have complex multiplication.Modular form 100800.2.a.a
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.