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SageMath
E = EllipticCurve("jx1")
E.isogeny_class()
Elliptic curves in class 145200jx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145200.bg1 | 145200jx1 | \([0, -1, 0, -34283, -610938]\) | \(10061824/5445\) | \(2411537411250000\) | \([2]\) | \(737280\) | \(1.6426\) | \(\Gamma_0(N)\)-optimal |
145200.bg2 | 145200jx2 | \([0, -1, 0, 132092, -4936688]\) | \(35969456/22275\) | \(-157846085100000000\) | \([2]\) | \(1474560\) | \(1.9892\) |
Rank
sage: E.rank()
The elliptic curves in class 145200jx have rank \(0\).
Complex multiplication
The elliptic curves in class 145200jx do not have complex multiplication.Modular form 145200.2.a.jx
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.