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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 162288.cg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162288.cg1 | 162288w2 | \([0, 0, 0, -98931, 10064306]\) | \(304821217/51842\) | \(18211992555036672\) | \([2]\) | \(1327104\) | \(1.8407\) | |
162288.cg2 | 162288w1 | \([0, 0, 0, -28371, -1690990]\) | \(7189057/644\) | \(226235932360704\) | \([2]\) | \(663552\) | \(1.4941\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162288.cg have rank \(1\).
Complex multiplication
The elliptic curves in class 162288.cg do not have complex multiplication.Modular form 162288.2.a.cg
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.