Show commands:
SageMath
E = EllipticCurve("fy1")
E.isogeny_class()
Elliptic curves in class 202800.fy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
202800.fy1 | 202800hl3 | \([0, 1, 0, -2372761408, 44485809477188]\) | \(19129597231400697604/26325\) | \(2033051950800000000\) | \([2]\) | \(49545216\) | \(3.6793\) | |
202800.fy2 | 202800hl2 | \([0, 1, 0, -148298908, 695040702188]\) | \(18681746265374416/693005625\) | \(13380023151202500000000\) | \([2, 2]\) | \(24772608\) | \(3.3327\) | |
202800.fy3 | 202800hl4 | \([0, 1, 0, -141454408, 762103113188]\) | \(-4053153720264484/903687890625\) | \(-69790861498556250000000000\) | \([2]\) | \(49545216\) | \(3.6793\) | |
202800.fy4 | 202800hl1 | \([0, 1, 0, -9697783, 9796740188]\) | \(83587439220736/13990184325\) | \(16881986902892231250000\) | \([2]\) | \(12386304\) | \(2.9861\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 202800.fy have rank \(0\).
Complex multiplication
The elliptic curves in class 202800.fy do not have complex multiplication.Modular form 202800.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.