Show commands:
SageMath
E = EllipticCurve("gj1")
E.isogeny_class()
Elliptic curves in class 58800gj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58800.e2 | 58800gj1 | \([0, -1, 0, -653, -9183]\) | \(-40960/27\) | \(-20329747200\) | \([]\) | \(54432\) | \(0.67887\) | \(\Gamma_0(N)\)-optimal |
58800.e1 | 58800gj2 | \([0, -1, 0, -59453, -5559903]\) | \(-30866268160/3\) | \(-2258860800\) | \([]\) | \(163296\) | \(1.2282\) |
Rank
sage: E.rank()
The elliptic curves in class 58800gj have rank \(1\).
Complex multiplication
The elliptic curves in class 58800gj do not have complex multiplication.Modular form 58800.2.a.gj
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 Cremona 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 Cremona labels.