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SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 363888.ea
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363888.ea1 | 363888ea4 | \([0, 0, 0, -1926086259, -32535812198878]\) | \(22501000029889239268/3620708343\) | \(127157691074266827168768\) | \([2]\) | \(141557760\) | \(3.8357\) | |
| 363888.ea2 | 363888ea2 | \([0, 0, 0, -120746919, -505120560730]\) | \(22174957026242512/278654127129\) | \(2446552722379747409438976\) | \([2, 2]\) | \(70778880\) | \(3.4891\) | |
| 363888.ea3 | 363888ea3 | \([0, 0, 0, -20742699, -1316454797590]\) | \(-28104147578308/21301741002339\) | \(-748107813476945816694180864\) | \([2]\) | \(141557760\) | \(3.8357\) | |
| 363888.ea4 | 363888ea1 | \([0, 0, 0, -14163474, 8036093567]\) | \(572616640141312/280535480757\) | \(153941925076084881399888\) | \([2]\) | \(35389440\) | \(3.1425\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 363888.ea have rank \(0\).
Complex multiplication
The elliptic curves in class 363888.ea do not have complex multiplication.Modular form 363888.2.a.ea
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.
