Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 163990.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
163990.v1 | 163990l2 | \([1, 1, 1, -563925, 162762035]\) | \(133974081659809/192200\) | \(28452497865800\) | \([2]\) | \(1182720\) | \(1.8527\) | |
163990.v2 | 163990l1 | \([1, 1, 1, -34925, 2580835]\) | \(-31824875809/1240000\) | \(-183564502360000\) | \([2]\) | \(591360\) | \(1.5061\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 163990.v have rank \(0\).
Complex multiplication
The elliptic curves in class 163990.v do not have complex multiplication.Modular form 163990.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.