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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 78144ck
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78144.bb2 | 78144ck1 | \([0, -1, 0, -39253, -2967611]\) | \(6532108386304000/31987847133\) | \(32755555464192\) | \([2]\) | \(184320\) | \(1.4413\) | \(\Gamma_0(N)\)-optimal |
| 78144.bb1 | 78144ck2 | \([0, -1, 0, -627313, -191029199]\) | \(1666315860501346000/40252707\) | \(659500351488\) | \([2]\) | \(368640\) | \(1.7879\) |
Rank
sage: E.rank()
The elliptic curves in class 78144ck have rank \(0\).
Complex multiplication
The elliptic curves in class 78144ck do not have complex multiplication.Modular form 78144.2.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.
