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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 46200bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46200.u3 | 46200bx1 | \([0, -1, 0, -1783, 25312]\) | \(2508888064/396165\) | \(99041250000\) | \([4]\) | \(36864\) | \(0.83266\) | \(\Gamma_0(N)\)-optimal |
46200.u2 | 46200bx2 | \([0, -1, 0, -7908, -244188]\) | \(13674725584/1334025\) | \(5336100000000\) | \([2, 2]\) | \(73728\) | \(1.1792\) | |
46200.u4 | 46200bx3 | \([0, -1, 0, 9592, -1189188]\) | \(6099383804/41507235\) | \(-664115760000000\) | \([2]\) | \(147456\) | \(1.5258\) | |
46200.u1 | 46200bx4 | \([0, -1, 0, -123408, -16645188]\) | \(12990838708516/144375\) | \(2310000000000\) | \([2]\) | \(147456\) | \(1.5258\) |
Rank
sage: E.rank()
The elliptic curves in class 46200bx have rank \(1\).
Complex multiplication
The elliptic curves in class 46200bx do not have complex multiplication.Modular form 46200.2.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 Cremona 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 Cremona labels.