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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 27600.co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27600.co1 | 27600t2 | \([0, 1, 0, -12968008, -17978836012]\) | \(7536914291382802562/17961229575\) | \(574759346400000000\) | \([2]\) | \(1013760\) | \(2.6491\) | |
27600.co2 | 27600t1 | \([0, 1, 0, -801008, -288018012]\) | \(-3552342505518244/179863605135\) | \(-2877817682160000000\) | \([2]\) | \(506880\) | \(2.3026\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 27600.co have rank \(0\).
Complex multiplication
The elliptic curves in class 27600.co do not have complex multiplication.Modular form 27600.2.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 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.