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SageMath
E = EllipticCurve("jy1")
E.isogeny_class()
Elliptic curves in class 436800jy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
436800.jy2 | 436800jy1 | \([0, -1, 0, 1142367, 5309539137]\) | \(40251338884511/2997011332224\) | \(-12275758416789504000000\) | \([]\) | \(31610880\) | \(2.9180\) | \(\Gamma_0(N)\)-optimal* |
436800.jy1 | 436800jy2 | \([0, -1, 0, -5879193633, 173512059571137]\) | \(-5486773802537974663600129/2635437714\) | \(-10794752876544000000\) | \([]\) | \(221276160\) | \(3.8910\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 436800jy have rank \(1\).
Complex multiplication
The elliptic curves in class 436800jy do not have complex multiplication.Modular form 436800.2.a.jy
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.