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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 58800.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58800.bx1 | 58800fj4 | \([0, -1, 0, -2205408, -1259786688]\) | \(157551496201/13125\) | \(98825160000000000\) | \([2]\) | \(1179648\) | \(2.3049\) | |
58800.bx2 | 58800fj2 | \([0, -1, 0, -147408, -16754688]\) | \(47045881/11025\) | \(83013134400000000\) | \([2, 2]\) | \(589824\) | \(1.9583\) | |
58800.bx3 | 58800fj1 | \([0, -1, 0, -49408, 4021312]\) | \(1771561/105\) | \(790601280000000\) | \([2]\) | \(294912\) | \(1.6117\) | \(\Gamma_0(N)\)-optimal |
58800.bx4 | 58800fj3 | \([0, -1, 0, 342592, -104954688]\) | \(590589719/972405\) | \(-7321758454080000000\) | \([2]\) | \(1179648\) | \(2.3049\) |
Rank
sage: E.rank()
The elliptic curves in class 58800.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 58800.bx do not have complex multiplication.Modular form 58800.2.a.bx
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.