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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 203840cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203840.ez4 | 203840cs1 | \([0, -1, 0, -732321, 241138241]\) | \(1408317602329/2153060\) | \(66402479227535360\) | \([2]\) | \(2654208\) | \(2.1275\) | \(\Gamma_0(N)\)-optimal |
| 203840.ez3 | 203840cs2 | \([0, -1, 0, -951841, 84883905]\) | \(3092354182009/1689383150\) | \(52102231022462566400\) | \([2]\) | \(5308416\) | \(2.4741\) | |
| 203840.ez2 | 203840cs3 | \([0, -1, 0, -2974561, -1738433535]\) | \(94376601570889/12235496000\) | \(377354680769970176000\) | \([2]\) | \(7962624\) | \(2.6768\) | |
| 203840.ez1 | 203840cs4 | \([0, -1, 0, -46000481, -120068318719]\) | \(349046010201856969/7245875000\) | \(223469882015744000000\) | \([2]\) | \(15925248\) | \(3.0234\) |
Rank
sage: E.rank()
The elliptic curves in class 203840cs have rank \(0\).
Complex multiplication
The elliptic curves in class 203840cs do not have complex multiplication.Modular form 203840.2.a.cs
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.
