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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 66240.eu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66240.eu1 | 66240ct2 | \([0, 0, 0, -18673932, -31059959056]\) | \(7536914291382802562/17961229575\) | \(1716222212200857600\) | \([2]\) | \(2703360\) | \(2.7403\) | |
66240.eu2 | 66240ct1 | \([0, 0, 0, -1153452, -497233744]\) | \(-3552342505518244/179863605135\) | \(-8593117553846845440\) | \([2]\) | \(1351680\) | \(2.3937\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 66240.eu have rank \(0\).
Complex multiplication
The elliptic curves in class 66240.eu do not have complex multiplication.Modular form 66240.2.a.eu
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.