Show commands:
SageMath
E = EllipticCurve("lj1")
E.isogeny_class()
Elliptic curves in class 100800lj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.fp2 | 100800lj1 | \([0, 0, 0, -75, 61000]\) | \(-64/2205\) | \(-1607445000000\) | \([2]\) | \(147456\) | \(1.0210\) | \(\Gamma_0(N)\)-optimal |
100800.fp1 | 100800lj2 | \([0, 0, 0, -23700, 1384000]\) | \(31554496/525\) | \(24494400000000\) | \([2]\) | \(294912\) | \(1.3676\) |
Rank
sage: E.rank()
The elliptic curves in class 100800lj have rank \(1\).
Complex multiplication
The elliptic curves in class 100800lj do not have complex multiplication.Modular form 100800.2.a.lj
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 Cremona 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 Cremona labels.