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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 600.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 600.c1 | 600a5 | \([0, -1, 0, -80008, -8683988]\) | \(1770025017602/75\) | \(2400000000\) | \([2]\) | \(1536\) | \(1.2847\) | |
| 600.c2 | 600a3 | \([0, -1, 0, -5008, -133988]\) | \(868327204/5625\) | \(90000000000\) | \([2, 2]\) | \(768\) | \(0.93814\) | |
| 600.c3 | 600a6 | \([0, -1, 0, -2008, -295988]\) | \(-27995042/1171875\) | \(-37500000000000\) | \([2]\) | \(1536\) | \(1.2847\) | |
| 600.c4 | 600a2 | \([0, -1, 0, -508, 1012]\) | \(3631696/2025\) | \(8100000000\) | \([2, 2]\) | \(384\) | \(0.59157\) | |
| 600.c5 | 600a1 | \([0, -1, 0, -383, 3012]\) | \(24918016/45\) | \(11250000\) | \([4]\) | \(192\) | \(0.24500\) | \(\Gamma_0(N)\)-optimal |
| 600.c6 | 600a4 | \([0, -1, 0, 1992, 6012]\) | \(54607676/32805\) | \(-524880000000\) | \([2]\) | \(768\) | \(0.93814\) |
Rank
sage: E.rank()
The elliptic curves in class 600.c have rank \(1\).
Complex multiplication
The elliptic curves in class 600.c do not have complex multiplication.Modular form 600.2.a.c
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
