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SageMath
E = EllipticCurve("fy1")
E.isogeny_class()
Elliptic curves in class 92400.fy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92400.fy1 | 92400gi2 | \([0, 1, 0, -36229908, 83913539688]\) | \(1314817350433665559504/190690249278375\) | \(762760997113500000000\) | \([2]\) | \(7741440\) | \(3.0219\) | |
92400.fy2 | 92400gi1 | \([0, 1, 0, -2058033, 1559320938]\) | \(-3856034557002072064/1973796785296875\) | \(-493449196324218750000\) | \([2]\) | \(3870720\) | \(2.6753\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.fy have rank \(0\).
Complex multiplication
The elliptic curves in class 92400.fy do not have complex multiplication.Modular form 92400.2.a.fy
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.