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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 84150cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84150.y3 | 84150cs1 | \([1, -1, 0, -9876942, -20218554284]\) | \(-9354997870579612441/10093752054144000\) | \(-114974144491734000000000\) | \([2]\) | \(8847360\) | \(3.1198\) | \(\Gamma_0(N)\)-optimal |
| 84150.y2 | 84150cs2 | \([1, -1, 0, -186744942, -981849870284]\) | \(63229930193881628103961/26218934428500000\) | \(298650049974632812500000\) | \([2]\) | \(17694720\) | \(3.4664\) | |
| 84150.y4 | 84150cs3 | \([1, -1, 0, 82783683, 365186246341]\) | \(5508208700580085578359/8246033269590589440\) | \(-93927472711430307840000000\) | \([2]\) | \(26542080\) | \(3.6691\) | |
| 84150.y1 | 84150cs4 | \([1, -1, 0, -543904317, 3669712070341]\) | \(1562225332123379392365961/393363080510106009600\) | \(4480651338935426265600000000\) | \([2]\) | \(53084160\) | \(4.0157\) |
Rank
sage: E.rank()
The elliptic curves in class 84150cs have rank \(0\).
Complex multiplication
The elliptic curves in class 84150cs do not have complex multiplication.Modular form 84150.2.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.
