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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 67280.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67280.d1 | 67280p2 | \([0, 1, 0, -605668296, 5012247371380]\) | \(14258975033569/1953125000\) | \(3365657866401608000000000000\) | \([]\) | \(27060480\) | \(4.0088\) | |
67280.d2 | 67280p1 | \([0, 1, 0, -153008456, -727660463756]\) | \(229895296609/320000\) | \(551429384831239454720000\) | \([]\) | \(9020160\) | \(3.4595\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 67280.d have rank \(0\).
Complex multiplication
The elliptic curves in class 67280.d do not have complex multiplication.Modular form 67280.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.