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SageMath
E = EllipticCurve("hx1")
E.isogeny_class()
Elliptic curves in class 169050.hx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 169050.hx1 | 169050bh4 | \([1, 0, 0, -3692956688, -237272203008]\) | \(3029968325354577848895529/1753440696000000000000\) | \(3223289756932875000000000000000\) | \([2]\) | \(318504960\) | \(4.5435\) | |
| 169050.hx2 | 169050bh2 | \([1, 0, 0, -2540458313, -49285104061383]\) | \(986396822567235411402169/6336721794060000\) | \(11648577849208827187500000\) | \([2]\) | \(106168320\) | \(3.9942\) | |
| 169050.hx3 | 169050bh1 | \([1, 0, 0, -155726313, -801117769383]\) | \(-227196402372228188089/19338934824115200\) | \(-35550099111286393200000000\) | \([2]\) | \(53084160\) | \(3.6476\) | \(\Gamma_0(N)\)-optimal |
| 169050.hx4 | 169050bh3 | \([1, 0, 0, 923235312, -29543563008]\) | \(47342661265381757089751/27397579603968000000\) | \(-50364028794175488000000000000\) | \([2]\) | \(159252480\) | \(4.1969\) |
Rank
sage: E.rank()
The elliptic curves in class 169050.hx have rank \(0\).
Complex multiplication
The elliptic curves in class 169050.hx do not have complex multiplication.Modular form 169050.2.a.hx
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
