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SageMath
E = EllipticCurve("lj1")
E.isogeny_class()
Elliptic curves in class 187200.lj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
187200.lj1 | 187200fh2 | \([0, 0, 0, -662700, -186014000]\) | \(10779215329/1232010\) | \(3678762147840000000\) | \([2]\) | \(3538944\) | \(2.2947\) | |
187200.lj2 | 187200fh1 | \([0, 0, 0, 57300, -14654000]\) | \(6967871/35100\) | \(-104808038400000000\) | \([2]\) | \(1769472\) | \(1.9481\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 187200.lj have rank \(1\).
Complex multiplication
The elliptic curves in class 187200.lj do not have complex multiplication.Modular form 187200.2.a.lj
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.