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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 84150.co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84150.co1 | 84150bp2 | \([1, -1, 0, -32292, -1418634]\) | \(326940373369/112003650\) | \(1275791575781250\) | \([2]\) | \(393216\) | \(1.6005\) | |
84150.co2 | 84150bp1 | \([1, -1, 0, 5958, -156384]\) | \(2053225511/2098140\) | \(-23899125937500\) | \([2]\) | \(196608\) | \(1.2539\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 84150.co have rank \(1\).
Complex multiplication
The elliptic curves in class 84150.co do not have complex multiplication.Modular form 84150.2.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.