Show commands:
SageMath
E = EllipticCurve("jd1")
E.isogeny_class()
Elliptic curves in class 100800.jd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.jd1 | 100800bg2 | \([0, 0, 0, -78300, 8262000]\) | \(10536048/245\) | \(1234517760000000\) | \([2]\) | \(442368\) | \(1.6817\) | |
100800.jd2 | 100800bg1 | \([0, 0, 0, -10800, -243000]\) | \(442368/175\) | \(55112400000000\) | \([2]\) | \(221184\) | \(1.3351\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100800.jd have rank \(0\).
Complex multiplication
The elliptic curves in class 100800.jd do not have complex multiplication.Modular form 100800.2.a.jd
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.