Show commands:
SageMath
E = EllipticCurve("jn1")
E.isogeny_class()
Elliptic curves in class 187200.jn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
187200.jn1 | 187200mu2 | \([0, 0, 0, -61500, 5866000]\) | \(137842000/117\) | \(21835008000000\) | \([2]\) | \(589824\) | \(1.4867\) | |
187200.jn2 | 187200mu1 | \([0, 0, 0, -3000, 133000]\) | \(-256000/507\) | \(-5913648000000\) | \([2]\) | \(294912\) | \(1.1402\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 187200.jn have rank \(0\).
Complex multiplication
The elliptic curves in class 187200.jn do not have complex multiplication.Modular form 187200.2.a.jn
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.