Show commands:
SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 439280dt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
439280.dt1 | 439280dt1 | \([0, -1, 0, -266265, -49232488]\) | \(5405726654464/407253125\) | \(157281606482450000\) | \([2]\) | \(4915200\) | \(2.0450\) | \(\Gamma_0(N)\)-optimal |
439280.dt2 | 439280dt2 | \([0, -1, 0, 255380, -219080100]\) | \(298091207216/3525390625\) | \(-21784156022500000000\) | \([2]\) | \(9830400\) | \(2.3916\) |
Rank
sage: E.rank()
The elliptic curves in class 439280dt have rank \(0\).
Complex multiplication
The elliptic curves in class 439280dt do not have complex multiplication.Modular form 439280.2.a.dt
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.