Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 41650.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41650.l1 | 41650bd1 | \([1, 1, 0, -1681950, -840333500]\) | \(-4768951705/272\) | \(-30012995206250000\) | \([]\) | \(483840\) | \(2.2256\) | \(\Gamma_0(N)\)-optimal |
41650.l2 | 41650bd2 | \([1, 1, 0, -181325, -2267427875]\) | \(-5975305/20123648\) | \(-2220481437339200000000\) | \([]\) | \(1451520\) | \(2.7749\) |
Rank
sage: E.rank()
The elliptic curves in class 41650.l have rank \(0\).
Complex multiplication
The elliptic curves in class 41650.l do not have complex multiplication.Modular form 41650.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.