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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 228888.ck
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 228888.ck1 | 228888y1 | \([0, 0, 0, -20850483, 36645624830]\) | \(55635379958596/24057\) | \(433473429123744768\) | \([2]\) | \(12386304\) | \(2.7266\) | \(\Gamma_0(N)\)-optimal |
| 228888.ck2 | 228888y2 | \([0, 0, 0, -20746443, 37029428390]\) | \(-27403349188178/578739249\) | \(-20856140568859855767552\) | \([2]\) | \(24772608\) | \(3.0732\) |
Rank
sage: E.rank()
The elliptic curves in class 228888.ck have rank \(1\).
Complex multiplication
The elliptic curves in class 228888.ck do not have complex multiplication.Modular form 228888.2.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 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.
