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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 163800co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
163800.bt1 | 163800co1 | \([0, 0, 0, -28950, -1892875]\) | \(397526095872/739375\) | \(4990781250000\) | \([2]\) | \(344064\) | \(1.3272\) | \(\Gamma_0(N)\)-optimal |
163800.bt2 | 163800co2 | \([0, 0, 0, -19575, -3139750]\) | \(-7680778992/34987225\) | \(-3778620300000000\) | \([2]\) | \(688128\) | \(1.6738\) |
Rank
sage: E.rank()
The elliptic curves in class 163800co have rank \(0\).
Complex multiplication
The elliptic curves in class 163800co do not have complex multiplication.Modular form 163800.2.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.