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SageMath
E = EllipticCurve("oq1")
E.isogeny_class()
Elliptic curves in class 187200.oq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
187200.oq1 | 187200oa3 | \([0, 0, 0, -2988300, 1908502000]\) | \(988345570681/44994560\) | \(134353036247040000000\) | \([2]\) | \(7962624\) | \(2.6242\) | |
187200.oq2 | 187200oa1 | \([0, 0, 0, -468300, -122618000]\) | \(3803721481/26000\) | \(77635584000000000\) | \([2]\) | \(2654208\) | \(2.0749\) | \(\Gamma_0(N)\)-optimal |
187200.oq3 | 187200oa2 | \([0, 0, 0, -180300, -271802000]\) | \(-217081801/10562500\) | \(-31539456000000000000\) | \([2]\) | \(5308416\) | \(2.4215\) | |
187200.oq4 | 187200oa4 | \([0, 0, 0, 1619700, 7262998000]\) | \(157376536199/7722894400\) | \(-23060439112089600000000\) | \([2]\) | \(15925248\) | \(2.9708\) |
Rank
sage: E.rank()
The elliptic curves in class 187200.oq have rank \(1\).
Complex multiplication
The elliptic curves in class 187200.oq do not have complex multiplication.Modular form 187200.2.a.oq
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.