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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 200400cy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
200400.bg2 | 200400cy1 | \([0, -1, 0, -26708, -1913088]\) | \(-4213995536/753003\) | \(-376501500000000\) | \([2]\) | \(821760\) | \(1.5222\) | \(\Gamma_0(N)\)-optimal |
200400.bg1 | 200400cy2 | \([0, -1, 0, -444208, -113803088]\) | \(4846785739124/121743\) | \(243486000000000\) | \([2]\) | \(1643520\) | \(1.8688\) |
Rank
sage: E.rank()
The elliptic curves in class 200400cy have rank \(0\).
Complex multiplication
The elliptic curves in class 200400cy do not have complex multiplication.Modular form 200400.2.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.