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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 127296.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127296.k1 | 127296dw1 | \([0, 0, 0, -15276, -708784]\) | \(8251733668/232713\) | \(11118036713472\) | \([2]\) | \(458752\) | \(1.2821\) | \(\Gamma_0(N)\)-optimal |
127296.k2 | 127296dw2 | \([0, 0, 0, 3444, -2333680]\) | \(47279806/24649677\) | \(-2355313316069376\) | \([2]\) | \(917504\) | \(1.6287\) |
Rank
sage: E.rank()
The elliptic curves in class 127296.k have rank \(1\).
Complex multiplication
The elliptic curves in class 127296.k do not have complex multiplication.Modular form 127296.2.a.k
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.