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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 156090bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
156090.o1 | 156090bq1 | \([1, 0, 1, -23114, -1248964]\) | \(770842973809/66873600\) | \(118470661689600\) | \([2]\) | \(896000\) | \(1.4412\) | \(\Gamma_0(N)\)-optimal |
156090.o2 | 156090bq2 | \([1, 0, 1, 25286, -5779204]\) | \(1009328859791/8734528080\) | \(-15473749299932880\) | \([2]\) | \(1792000\) | \(1.7878\) |
Rank
sage: E.rank()
The elliptic curves in class 156090bq have rank \(0\).
Complex multiplication
The elliptic curves in class 156090bq do not have complex multiplication.Modular form 156090.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.