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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 62400cx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62400.er3 | 62400cx1 | \([0, 1, 0, -9633, 2332863]\) | \(-24137569/561600\) | \(-2300313600000000\) | \([2]\) | \(221184\) | \(1.6284\) | \(\Gamma_0(N)\)-optimal |
| 62400.er2 | 62400cx2 | \([0, 1, 0, -329633, 72412863]\) | \(967068262369/4928040\) | \(20185251840000000\) | \([2]\) | \(442368\) | \(1.9750\) | |
| 62400.er4 | 62400cx3 | \([0, 1, 0, 86367, -61699137]\) | \(17394111071/411937500\) | \(-1687296000000000000\) | \([2]\) | \(663552\) | \(2.1777\) | |
| 62400.er1 | 62400cx4 | \([0, 1, 0, -1913633, -967699137]\) | \(189208196468929/10860320250\) | \(44483871744000000000\) | \([2]\) | \(1327104\) | \(2.5243\) |
Rank
sage: E.rank()
The elliptic curves in class 62400cx have rank \(1\).
Complex multiplication
The elliptic curves in class 62400cx do not have complex multiplication.Modular form 62400.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
