Show commands:
SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 78400ck
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78400.ki2 | 78400ck1 | \([0, -1, 0, -5568033, -5945332063]\) | \(-115501303/25600\) | \(-4231382381363200000000\) | \([2]\) | \(5160960\) | \(2.8702\) | \(\Gamma_0(N)\)-optimal |
| 78400.ki1 | 78400ck2 | \([0, -1, 0, -93376033, -347255028063]\) | \(544737993463/20000\) | \(3305767485440000000000\) | \([2]\) | \(10321920\) | \(3.2168\) |
Rank
sage: E.rank()
The elliptic curves in class 78400ck have rank \(0\).
Complex multiplication
The elliptic curves in class 78400ck do not have complex multiplication.Modular form 78400.2.a.ck
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.
