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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 164934.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 164934.y1 | 164934dh3 | \([1, -1, 0, -7318204497, -240963702558755]\) | \(505384091400037554067434625/815656731648\) | \(69955713940986897408\) | \([2]\) | \(99532800\) | \(3.9632\) | |
| 164934.y2 | 164934dh4 | \([1, -1, 0, -7318133937, -240968581542851]\) | \(-505369473241574671219626625/20303219722982711328\) | \(-1741328399450921700665318688\) | \([2]\) | \(199065600\) | \(4.3098\) | |
| 164934.y3 | 164934dh1 | \([1, -1, 0, -90602577, -328565031971]\) | \(959024269496848362625/11151660319506432\) | \(956434648313687307190272\) | \([2]\) | \(33177600\) | \(3.4139\) | \(\Gamma_0(N)\)-optimal |
| 164934.y4 | 164934dh2 | \([1, -1, 0, -18349137, -838226347043]\) | \(-7966267523043306625/3534510366354604032\) | \(-303141243756523298315599872\) | \([2]\) | \(66355200\) | \(3.7605\) |
Rank
sage: E.rank()
The elliptic curves in class 164934.y have rank \(1\).
Complex multiplication
The elliptic curves in class 164934.y do not have complex multiplication.Modular form 164934.2.a.y
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
