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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 63162ck
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63162.bz2 | 63162ck1 | \([1, -1, 1, -1112, 4926683]\) | \(-117649/8118144\) | \(-10484322943729536\) | \([]\) | \(313600\) | \(1.7529\) | \(\Gamma_0(N)\)-optimal |
| 63162.bz1 | 63162ck2 | \([1, -1, 1, -7090502, -7286625277]\) | \(-30526075007211889/103499257854\) | \(-133665976333712678526\) | \([]\) | \(2195200\) | \(2.7259\) |
Rank
sage: E.rank()
The elliptic curves in class 63162ck have rank \(1\).
Complex multiplication
The elliptic curves in class 63162ck do not have complex multiplication.Modular form 63162.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
