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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 13200.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13200.bi1 | 13200bm3 | \([0, -1, 0, -58608, -5436288]\) | \(347873904937/395307\) | \(25299648000000\) | \([2]\) | \(49152\) | \(1.4852\) | |
13200.bi2 | 13200bm2 | \([0, -1, 0, -4608, -36288]\) | \(169112377/88209\) | \(5645376000000\) | \([2, 2]\) | \(24576\) | \(1.1387\) | |
13200.bi3 | 13200bm1 | \([0, -1, 0, -2608, 51712]\) | \(30664297/297\) | \(19008000000\) | \([2]\) | \(12288\) | \(0.79209\) | \(\Gamma_0(N)\)-optimal |
13200.bi4 | 13200bm4 | \([0, -1, 0, 17392, -300288]\) | \(9090072503/5845851\) | \(-374134464000000\) | \([2]\) | \(49152\) | \(1.4852\) |
Rank
sage: E.rank()
The elliptic curves in class 13200.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 13200.bi do not have complex multiplication.Modular form 13200.2.a.bi
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.