Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 464c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
464.e2 | 464c1 | \([0, 1, 0, 80, -428]\) | \(13651919/29696\) | \(-121634816\) | \([]\) | \(96\) | \(0.23559\) | \(\Gamma_0(N)\)-optimal |
464.e1 | 464c2 | \([0, 1, 0, -7280, 238292]\) | \(-10418796526321/82044596\) | \(-336054665216\) | \([]\) | \(480\) | \(1.0403\) |
Rank
sage: E.rank()
The elliptic curves in class 464c have rank \(0\).
Complex multiplication
The elliptic curves in class 464c do not have complex multiplication.Modular form 464.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.