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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 6384.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6384.a1 | 6384a2 | \([0, -1, 0, -320, 816]\) | \(3550014724/1842183\) | \(1886395392\) | \([2]\) | \(4608\) | \(0.47179\) | |
6384.a2 | 6384a1 | \([0, -1, 0, -180, -864]\) | \(2533446736/25137\) | \(6435072\) | \([2]\) | \(2304\) | \(0.12521\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6384.a have rank \(1\).
Complex multiplication
The elliptic curves in class 6384.a do not have complex multiplication.Modular form 6384.2.a.a
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.