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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 51600cy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51600.cb1 | 51600cy1 | \([0, 1, 0, -76408, -7520812]\) | \(770842973809/66873600\) | \(4279910400000000\) | \([2]\) | \(368640\) | \(1.7402\) | \(\Gamma_0(N)\)-optimal |
51600.cb2 | 51600cy2 | \([0, 1, 0, 83592, -34720812]\) | \(1009328859791/8734528080\) | \(-559009797120000000\) | \([2]\) | \(737280\) | \(2.0867\) |
Rank
sage: E.rank()
The elliptic curves in class 51600cy have rank \(1\).
Complex multiplication
The elliptic curves in class 51600cy do not have complex multiplication.Modular form 51600.2.a.cy
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.