Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 39270.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39270.o1 | 39270n2 | \([1, 1, 0, -106132022, -420884794284]\) | \(132209612899197312130102702441/60427081782342696960\) | \(60427081782342696960\) | \([2]\) | \(5591040\) | \(3.1347\) | |
39270.o2 | 39270n1 | \([1, 1, 0, -6599222, -6649187244]\) | \(-31783522700273801593467241/690414869906089574400\) | \(-690414869906089574400\) | \([2]\) | \(2795520\) | \(2.7882\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39270.o have rank \(0\).
Complex multiplication
The elliptic curves in class 39270.o do not have complex multiplication.Modular form 39270.2.a.o
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.