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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 193200.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193200.o1 | 193200hh3 | \([0, -1, 0, -70932008, 229149376512]\) | \(2466780454987534385284/10072750481768625\) | \(161164007708298000000000\) | \([4]\) | \(26542080\) | \(3.3089\) | |
| 193200.o2 | 193200hh2 | \([0, -1, 0, -6619508, -317623488]\) | \(8019382352783901136/4629798816890625\) | \(18519195267562500000000\) | \([2, 2]\) | \(13271040\) | \(2.9623\) | |
| 193200.o3 | 193200hh1 | \([0, -1, 0, -4666383, -3868404738]\) | \(44949507773962418176/132895751953125\) | \(33223937988281250000\) | \([2]\) | \(6635520\) | \(2.6157\) | \(\Gamma_0(N)\)-optimal |
| 193200.o4 | 193200hh4 | \([0, -1, 0, 26442992, -2565873488]\) | \(127801365439147434716/74135664409456125\) | \(-1186170630551298000000000\) | \([2]\) | \(26542080\) | \(3.3089\) |
Rank
sage: E.rank()
The elliptic curves in class 193200.o have rank \(0\).
Complex multiplication
The elliptic curves in class 193200.o do not have complex multiplication.Modular form 193200.2.a.o
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.
