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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 169050.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169050.t1 | 169050ih1 | \([1, 1, 0, -1320820750, -18476804343500]\) | \(138626767243242683688529/5300196249600\) | \(9743168571393600000000\) | \([2]\) | \(53084160\) | \(3.7105\) | \(\Gamma_0(N)\)-optimal |
169050.t2 | 169050ih2 | \([1, 1, 0, -1318860750, -18534371503500]\) | \(-138010547060620856386129/857302254769101120\) | \(-1575949265177030901045000000\) | \([2]\) | \(106168320\) | \(4.0571\) |
Rank
sage: E.rank()
The elliptic curves in class 169050.t have rank \(0\).
Complex multiplication
The elliptic curves in class 169050.t do not have complex multiplication.Modular form 169050.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.