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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 16560.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16560.u1 | 16560x2 | \([0, 0, 0, -30123, 1954522]\) | \(27333463470867/895491200\) | \(99034162790400\) | \([2]\) | \(43008\) | \(1.4590\) | |
16560.u2 | 16560x1 | \([0, 0, 0, 597, 105178]\) | \(212776173/43335680\) | \(-4792579522560\) | \([2]\) | \(21504\) | \(1.1124\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16560.u have rank \(0\).
Complex multiplication
The elliptic curves in class 16560.u do not have complex multiplication.Modular form 16560.2.a.u
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.