Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 172480.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
172480.v1 | 172480l1 | \([0, 1, 0, -5945, -180545]\) | \(-3937024/55\) | \(-324673592320\) | \([]\) | \(290304\) | \(1.0148\) | \(\Gamma_0(N)\)-optimal |
172480.v2 | 172480l2 | \([0, 1, 0, 21495, -888497]\) | \(186050816/166375\) | \(-982137616768000\) | \([]\) | \(870912\) | \(1.5641\) |
Rank
sage: E.rank()
The elliptic curves in class 172480.v have rank \(1\).
Complex multiplication
The elliptic curves in class 172480.v do not have complex multiplication.Modular form 172480.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.