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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 272090.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
272090.d1 | 272090d2 | \([1, 0, 1, -4245284, -2448239454]\) | \(1753007192038126081/478174101507200\) | \(2308055056721866524800\) | \([2]\) | \(19353600\) | \(2.8070\) | |
272090.d2 | 272090d1 | \([1, 0, 1, -1541284, 705706146]\) | \(83890194895342081/3958384640000\) | \(19106366605813760000\) | \([2]\) | \(9676800\) | \(2.4604\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 272090.d have rank \(0\).
Complex multiplication
The elliptic curves in class 272090.d do not have complex multiplication.Modular form 272090.2.a.d
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.