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SageMath
E = EllipticCurve("ju1")
E.isogeny_class()
Elliptic curves in class 397488.ju
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 397488.ju1 | 397488ju3 | \([0, 1, 0, -3452384784, -78080094933996]\) | \(-1956469094246217097/36641439744\) | \(-85227712434711144519696384\) | \([]\) | \(376233984\) | \(4.1000\) | |
| 397488.ju2 | 397488ju2 | \([0, 1, 0, -16101024, -238139775756]\) | \(-198461344537/10417365504\) | \(-24230713577448222694047744\) | \([]\) | \(125411328\) | \(3.5507\) | |
| 397488.ju3 | 397488ju1 | \([0, 1, 0, 1785936, 8736046164]\) | \(270840023/14329224\) | \(-33329666929491747569664\) | \([]\) | \(41803776\) | \(3.0014\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 397488.ju have rank \(0\).
Complex multiplication
The elliptic curves in class 397488.ju do not have complex multiplication.Modular form 397488.2.a.ju
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
