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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 132600.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 132600.o1 | 132600u4 | \([0, -1, 0, -1562408, -751165188]\) | \(26362547147244676/244298925\) | \(3908782800000000\) | \([2]\) | \(1769472\) | \(2.1555\) | |
| 132600.o2 | 132600u2 | \([0, -1, 0, -99908, -11140188]\) | \(27572037674704/2472575625\) | \(9890302500000000\) | \([2, 2]\) | \(884736\) | \(1.8089\) | |
| 132600.o3 | 132600u1 | \([0, -1, 0, -21783, 1047312]\) | \(4572531595264/776953125\) | \(194238281250000\) | \([2]\) | \(442368\) | \(1.4623\) | \(\Gamma_0(N)\)-optimal |
| 132600.o4 | 132600u3 | \([0, -1, 0, 112592, -52365188]\) | \(9865576607324/79640206425\) | \(-1274243302800000000\) | \([2]\) | \(1769472\) | \(2.1555\) |
Rank
sage: E.rank()
The elliptic curves in class 132600.o have rank \(0\).
Complex multiplication
The elliptic curves in class 132600.o do not have complex multiplication.Modular form 132600.2.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.
