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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 10944.ck
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10944.ck1 | 10944t3 | \([0, 0, 0, -27696, 1774082]\) | \(-50357871050752/19\) | \(-886464\) | \([]\) | \(10368\) | \(0.92932\) | |
| 10944.ck2 | 10944t2 | \([0, 0, 0, -336, 2522]\) | \(-89915392/6859\) | \(-320013504\) | \([]\) | \(3456\) | \(0.38001\) | |
| 10944.ck3 | 10944t1 | \([0, 0, 0, 24, 2]\) | \(32768/19\) | \(-886464\) | \([]\) | \(1152\) | \(-0.16929\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10944.ck have rank \(0\).
Complex multiplication
The elliptic curves in class 10944.ck do not have complex multiplication.Modular form 10944.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
