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SageMath
E = EllipticCurve("ff1")
E.isogeny_class()
Elliptic curves in class 259182.ff
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259182.ff1 | 259182ff2 | \([1, -1, 1, -150277304, 709106072491]\) | \(8086832279405361/226576\) | \(10515728489856902928\) | \([2]\) | \(32440320\) | \(3.1607\) | |
259182.ff2 | 259182ff1 | \([1, -1, 1, -9404264, 11051984683]\) | \(1981858514481/10449152\) | \(484960655061635993856\) | \([2]\) | \(16220160\) | \(2.8141\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259182.ff have rank \(0\).
Complex multiplication
The elliptic curves in class 259182.ff do not have complex multiplication.Modular form 259182.2.a.ff
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.