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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 66240.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66240.j1 | 66240h2 | \([0, 0, 0, -11628, 464752]\) | \(196528293144/8265625\) | \(7312896000000\) | \([2]\) | \(159744\) | \(1.2331\) | |
66240.j2 | 66240h1 | \([0, 0, 0, -11508, 475168]\) | \(1524051208512/2875\) | \(317952000\) | \([2]\) | \(79872\) | \(0.88649\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 66240.j have rank \(1\).
Complex multiplication
The elliptic curves in class 66240.j do not have complex multiplication.Modular form 66240.2.a.j
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.