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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 148225.co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
148225.co1 | 148225cp2 | \([1, 1, 0, -373650, -343810375]\) | \(-121\) | \(-47679876045047640625\) | \([]\) | \(3326400\) | \(2.4587\) | |
148225.co2 | 148225cp1 | \([1, 1, 0, -36775, 2699250]\) | \(-24729001\) | \(-222430140625\) | \([]\) | \(302400\) | \(1.2597\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 148225.co have rank \(1\).
Complex multiplication
The elliptic curves in class 148225.co do not have complex multiplication.Modular form 148225.2.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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.