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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 93600.dq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93600.dq1 | 93600bn2 | \([0, 0, 0, -9075, 89750]\) | \(14172488/7605\) | \(44352360000000\) | \([2]\) | \(147456\) | \(1.3098\) | |
93600.dq2 | 93600bn1 | \([0, 0, 0, 2175, 11000]\) | \(1560896/975\) | \(-710775000000\) | \([2]\) | \(73728\) | \(0.96321\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 93600.dq have rank \(1\).
Complex multiplication
The elliptic curves in class 93600.dq do not have complex multiplication.Modular form 93600.2.a.dq
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.