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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 136242bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
136242.t2 | 136242bq1 | \([1, -1, 0, 3627, 7477]\) | \(109503/64\) | \(-3083564096064\) | \([]\) | \(275184\) | \(1.0858\) | \(\Gamma_0(N)\)-optimal |
136242.t1 | 136242bq2 | \([1, -1, 0, -46833, -4247983]\) | \(-35937/4\) | \(-1264454002142244\) | \([]\) | \(825552\) | \(1.6351\) |
Rank
sage: E.rank()
The elliptic curves in class 136242bq have rank \(1\).
Complex multiplication
The elliptic curves in class 136242bq do not have complex multiplication.Modular form 136242.2.a.bq
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.