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SageMath
E = EllipticCurve("fx1")
E.isogeny_class()
Elliptic curves in class 379050fx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
379050.fx1 | 379050fx1 | \([1, 1, 1, -61558, -5872669]\) | \(4386781853/27216\) | \(160050087162000\) | \([2]\) | \(2280960\) | \(1.5636\) | \(\Gamma_0(N)\)-optimal |
379050.fx2 | 379050fx2 | \([1, 1, 1, -25458, -12659469]\) | \(-310288733/11573604\) | \(-68061299565640500\) | \([2]\) | \(4561920\) | \(1.9101\) |
Rank
sage: E.rank()
The elliptic curves in class 379050fx have rank \(0\).
Complex multiplication
The elliptic curves in class 379050fx do not have complex multiplication.Modular form 379050.2.a.fx
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.