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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 9576.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9576.a1 | 9576o1 | \([0, 0, 0, -59967, 5635170]\) | \(4732922819952/16468459\) | \(82982061695232\) | \([2]\) | \(46080\) | \(1.5335\) | \(\Gamma_0(N)\)-optimal |
9576.a2 | 9576o2 | \([0, 0, 0, -33507, 10636110]\) | \(-206413976268/2305248169\) | \(-46463180503477248\) | \([2]\) | \(92160\) | \(1.8801\) |
Rank
sage: E.rank()
The elliptic curves in class 9576.a have rank \(1\).
Complex multiplication
The elliptic curves in class 9576.a do not have complex multiplication.Modular form 9576.2.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.