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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 72600co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72600.bq1 | 72600co1 | \([0, -1, 0, -25208, -447588]\) | \(62500/33\) | \(935384208000000\) | \([2]\) | \(276480\) | \(1.5642\) | \(\Gamma_0(N)\)-optimal |
72600.bq2 | 72600co2 | \([0, -1, 0, 95792, -3593588]\) | \(1714750/1089\) | \(-61735357728000000\) | \([2]\) | \(552960\) | \(1.9108\) |
Rank
sage: E.rank()
The elliptic curves in class 72600co have rank \(1\).
Complex multiplication
The elliptic curves in class 72600co do not have complex multiplication.Modular form 72600.2.a.co
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.