Show commands:
SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 39600.co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39600.co1 | 39600cj2 | \([0, 0, 0, -30375, 1181250]\) | \(314928/121\) | \(1190821500000000\) | \([2]\) | \(138240\) | \(1.5919\) | |
39600.co2 | 39600cj1 | \([0, 0, 0, -13500, -590625]\) | \(442368/11\) | \(6766031250000\) | \([2]\) | \(69120\) | \(1.2453\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39600.co have rank \(1\).
Complex multiplication
The elliptic curves in class 39600.co do not have complex multiplication.Modular form 39600.2.a.co
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.