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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 142800.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142800.bm1 | 142800ev4 | \([0, -1, 0, -2031608, -1113894288]\) | \(14489843500598257/6246072\) | \(399748608000000\) | \([2]\) | \(2359296\) | \(2.1444\) | |
142800.bm2 | 142800ev3 | \([0, -1, 0, -271608, 28889712]\) | \(34623662831857/14438442312\) | \(924060307968000000\) | \([2]\) | \(2359296\) | \(2.1444\) | |
142800.bm3 | 142800ev2 | \([0, -1, 0, -127608, -17190288]\) | \(3590714269297/73410624\) | \(4698279936000000\) | \([2, 2]\) | \(1179648\) | \(1.7978\) | |
142800.bm4 | 142800ev1 | \([0, -1, 0, 392, -806288]\) | \(103823/4386816\) | \(-280756224000000\) | \([2]\) | \(589824\) | \(1.4513\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 142800.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 142800.bm do not have complex multiplication.Modular form 142800.2.a.bm
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.