Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 9576r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9576.k2 | 9576r1 | \([0, 0, 0, -675, -1458]\) | \(1687500/931\) | \(18764669952\) | \([2]\) | \(4608\) | \(0.66182\) | \(\Gamma_0(N)\)-optimal |
| 9576.k1 | 9576r2 | \([0, 0, 0, -8235, -287226]\) | \(1532121750/2527\) | \(101865351168\) | \([2]\) | \(9216\) | \(1.0084\) |
Rank
sage: E.rank()
The elliptic curves in class 9576r have rank \(0\).
Complex multiplication
The elliptic curves in class 9576r do not have complex multiplication.Modular form 9576.2.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 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.
