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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 127296.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127296.p1 | 127296bt2 | \([0, 0, 0, -52116996, 144816209696]\) | \(5242933647830934578368/87947613\) | \(262610165256192\) | \([2]\) | \(5308416\) | \(2.7627\) | |
127296.p2 | 127296bt1 | \([0, 0, 0, -3257211, 2262900980]\) | \(-81913199224986275392/10610127067761\) | \(-495026088473457216\) | \([2]\) | \(2654208\) | \(2.4161\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 127296.p have rank \(0\).
Complex multiplication
The elliptic curves in class 127296.p do not have complex multiplication.Modular form 127296.2.a.p
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.