Show commands:
SageMath
E = EllipticCurve("kc1")
E.isogeny_class()
Elliptic curves in class 202800.kc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202800.kc1 | 202800bi2 | \([0, 1, 0, -24601048, 43267845908]\) | \(666276475992821/58199166792\) | \(143829126176832884736000\) | \([2]\) | \(24772608\) | \(3.1841\) | |
| 202800.kc2 | 202800bi1 | \([0, 1, 0, -24060248, 45416985108]\) | \(623295446073461/5458752\) | \(13490356880572416000\) | \([2]\) | \(12386304\) | \(2.8376\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 202800.kc have rank \(0\).
Complex multiplication
The elliptic curves in class 202800.kc do not have complex multiplication.Modular form 202800.2.a.kc
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.
