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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 80850.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
80850.t1 | 80850bc2 | \([1, 1, 0, -149475, 45744525]\) | \(-5023028944825/9420668928\) | \(-692707674193920000\) | \([]\) | \(1469664\) | \(2.1132\) | |
80850.t2 | 80850bc1 | \([1, 1, 0, 15900, -1321200]\) | \(6045109175/13856832\) | \(-1018901517480000\) | \([]\) | \(489888\) | \(1.5639\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 80850.t have rank \(1\).
Complex multiplication
The elliptic curves in class 80850.t do not have complex multiplication.Modular form 80850.2.a.t
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.