Show commands:
SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 185130dn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185130.cq2 | 185130dn1 | \([1, -1, 0, 28836, 1642108]\) | \(2053225511/2098140\) | \(-2709680604477660\) | \([2]\) | \(983040\) | \(1.6481\) | \(\Gamma_0(N)\)-optimal |
185130.cq1 | 185130dn2 | \([1, -1, 0, -156294, 15230650]\) | \(326940373369/112003650\) | \(144649126386086850\) | \([2]\) | \(1966080\) | \(1.9947\) |
Rank
sage: E.rank()
The elliptic curves in class 185130dn have rank \(1\).
Complex multiplication
The elliptic curves in class 185130dn do not have complex multiplication.Modular form 185130.2.a.dn
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.