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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 379050.cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
379050.cx1 | 379050cx2 | \([1, 0, 1, -1471, 21578]\) | \(38966378665/8232\) | \(74293800\) | \([]\) | \(209952\) | \(0.50598\) | |
379050.cx2 | 379050cx1 | \([1, 0, 1, -46, -82]\) | \(1155865/378\) | \(3411450\) | \([]\) | \(69984\) | \(-0.043324\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 379050.cx have rank \(1\).
Complex multiplication
The elliptic curves in class 379050.cx do not have complex multiplication.Modular form 379050.2.a.cx
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.