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SageMath
E = EllipticCurve("je1")
E.isogeny_class()
Elliptic curves in class 277200.je
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.je1 | 277200je2 | \([0, 0, 0, -5128275, 3135181250]\) | \(1278763167594532/375974556419\) | \(4385367226071216000000\) | \([2]\) | \(11796480\) | \(2.8586\) | |
277200.je2 | 277200je1 | \([0, 0, 0, 861225, 326105750]\) | \(24226243449392/29774625727\) | \(-86822808619932000000\) | \([2]\) | \(5898240\) | \(2.5120\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277200.je have rank \(1\).
Complex multiplication
The elliptic curves in class 277200.je do not have complex multiplication.Modular form 277200.2.a.je
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.