Show commands:
SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 257600.dj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257600.dj1 | 257600dj2 | \([0, 0, 0, -381100, -90270000]\) | \(1494447319737/5411854\) | \(22166953984000000\) | \([2]\) | \(2359296\) | \(1.9974\) | |
257600.dj2 | 257600dj1 | \([0, 0, 0, -13100, -2686000]\) | \(-60698457/725788\) | \(-2972827648000000\) | \([2]\) | \(1179648\) | \(1.6509\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 257600.dj have rank \(0\).
Complex multiplication
The elliptic curves in class 257600.dj do not have complex multiplication.Modular form 257600.2.a.dj
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.