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SageMath
E = EllipticCurve("fo1")
E.isogeny_class()
Elliptic curves in class 344850fo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
344850.fo2 | 344850fo1 | \([1, 1, 1, -4404463, 3572343281]\) | \(-341370886042369/1817528220\) | \(-50310345483615937500\) | \([2]\) | \(17203200\) | \(2.6252\) | \(\Gamma_0(N)\)-optimal |
344850.fo1 | 344850fo2 | \([1, 1, 1, -70561213, 228108352781]\) | \(1403607530712116449/39475350\) | \(1092702976896093750\) | \([2]\) | \(34406400\) | \(2.9717\) |
Rank
sage: E.rank()
The elliptic curves in class 344850fo have rank \(1\).
Complex multiplication
The elliptic curves in class 344850fo do not have complex multiplication.Modular form 344850.2.a.fo
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.