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SageMath
E = EllipticCurve("es1")
E.isogeny_class()
Elliptic curves in class 202800.es
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
202800.es1 | 202800gl2 | \([0, -1, 0, -616258535208, 186205718225868912]\) | \(-134057911417971280740025/1872\) | \(-361431457920000000000\) | \([]\) | \(677376000\) | \(4.9244\) | |
202800.es2 | 202800gl1 | \([0, -1, 0, -960739368, 12557314089072]\) | \(-198417696411528597145/22989483914821632\) | \(-11362902821418627761386291200\) | \([]\) | \(135475200\) | \(4.1196\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 202800.es have rank \(0\).
Complex multiplication
The elliptic curves in class 202800.es do not have complex multiplication.Modular form 202800.2.a.es
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.