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SageMath
E = EllipticCurve("ed1")
E.isogeny_class()
Elliptic curves in class 115920.ed
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.ed1 | 115920bs4 | \([0, 0, 0, -596307, 177236386]\) | \(31412749404762436/7455105\) | \(5565206062080\) | \([4]\) | \(688128\) | \(1.8243\) | |
| 115920.ed2 | 115920bs2 | \([0, 0, 0, -37407, 2747806]\) | \(31018076123344/472410225\) | \(88163085830400\) | \([2, 2]\) | \(344064\) | \(1.4777\) | |
| 115920.ed3 | 115920bs1 | \([0, 0, 0, -4602, -53741]\) | \(924093773824/427810005\) | \(4989975898320\) | \([2]\) | \(172032\) | \(1.1312\) | \(\Gamma_0(N)\)-optimal |
| 115920.ed4 | 115920bs3 | \([0, 0, 0, -3387, 7558234]\) | \(-5756278756/33056218125\) | \(-24676334605440000\) | \([2]\) | \(688128\) | \(1.8243\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.ed have rank \(0\).
Complex multiplication
The elliptic curves in class 115920.ed do not have complex multiplication.Modular form 115920.2.a.ed
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
