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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 61200du
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61200.r2 | 61200du1 | \([0, 0, 0, -30675, -30480750]\) | \(-1847284083/231200000\) | \(-399513600000000000\) | \([2]\) | \(737280\) | \(2.0569\) | \(\Gamma_0(N)\)-optimal |
61200.r1 | 61200du2 | \([0, 0, 0, -1662675, -818736750]\) | \(294172502025843/2656250000\) | \(4590000000000000000\) | \([2]\) | \(1474560\) | \(2.4034\) |
Rank
sage: E.rank()
The elliptic curves in class 61200du have rank \(1\).
Complex multiplication
The elliptic curves in class 61200du do not have complex multiplication.Modular form 61200.2.a.du
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.