Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 6400.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6400.r1 | 6400n1 | \([0, 1, 0, -253, -1637]\) | \(-2194880\) | \(-819200\) | \([]\) | \(1152\) | \(0.091987\) | \(\Gamma_0(N)\)-optimal |
6400.r2 | 6400n2 | \([0, 1, 0, 1667, 7963]\) | \(1600\) | \(-320000000000\) | \([]\) | \(5760\) | \(0.89671\) |
Rank
sage: E.rank()
The elliptic curves in class 6400.r have rank \(0\).
Complex multiplication
The elliptic curves in class 6400.r do not have complex multiplication.Modular form 6400.2.a.r
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.