Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 203280.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
203280.l1 | 203280em2 | \([0, -1, 0, -74588136, -247879996560]\) | \(8417729709220226489459/1518688316880000\) | \(8279548517446778880000\) | \([2]\) | \(23224320\) | \(3.2094\) | |
203280.l2 | 203280em1 | \([0, -1, 0, -4188136, -4690236560]\) | \(-1490212288072889459/881798400000000\) | \(-4807367353958400000000\) | \([2]\) | \(11612160\) | \(2.8628\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 203280.l have rank \(0\).
Complex multiplication
The elliptic curves in class 203280.l do not have complex multiplication.Modular form 203280.2.a.l
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.