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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 73920.cx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.cx1 | 73920bb2 | \([0, -1, 0, -5796785, -5369307183]\) | \(1314817350433665559504/190690249278375\) | \(3124269044176896000\) | \([2]\) | \(2580480\) | \(2.5638\) | |
| 73920.cx2 | 73920bb1 | \([0, -1, 0, -329285, -99730683]\) | \(-3856034557002072064/1973796785296875\) | \(-2021167908144000000\) | \([2]\) | \(1290240\) | \(2.2172\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 73920.cx have rank \(1\).
Complex multiplication
The elliptic curves in class 73920.cx do not have complex multiplication.Modular form 73920.2.a.cx
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.
