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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 176400dy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.ck2 | 176400dy1 | \([0, 0, 0, -12528075, -20071759750]\) | \(-115501303/25600\) | \(-48198089937715200000000\) | \([2]\) | \(15482880\) | \(3.0729\) | \(\Gamma_0(N)\)-optimal |
176400.ck1 | 176400dy2 | \([0, 0, 0, -210096075, -1172090767750]\) | \(544737993463/20000\) | \(37654757763840000000000\) | \([2]\) | \(30965760\) | \(3.4195\) |
Rank
sage: E.rank()
The elliptic curves in class 176400dy have rank \(0\).
Complex multiplication
The elliptic curves in class 176400dy do not have complex multiplication.Modular form 176400.2.a.dy
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 Cremona 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 Cremona labels.