Show commands:
SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 38808.cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38808.cj1 | 38808ck2 | \([0, 0, 0, -10051419, 8602937350]\) | \(1278763167594532/375974556419\) | \(33019780401923359435776\) | \([2]\) | \(2211840\) | \(3.0268\) | |
38808.cj2 | 38808ck1 | \([0, 0, 0, 1688001, 894834178]\) | \(24226243449392/29774625727\) | \(-653735463124888311552\) | \([2]\) | \(1105920\) | \(2.6802\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38808.cj have rank \(1\).
Complex multiplication
The elliptic curves in class 38808.cj do not have complex multiplication.Modular form 38808.2.a.cj
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.