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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 157200bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
157200.cu2 | 157200bb1 | \([0, 1, 0, -854008, -289012012]\) | \(1076291879750641/60150618144\) | \(3849639561216000000\) | \([]\) | \(2822400\) | \(2.3212\) | \(\Gamma_0(N)\)-optimal |
157200.cu1 | 157200bb2 | \([0, 1, 0, -90818008, 333093379988]\) | \(1294373635812597347281/2083292441154\) | \(133330716233856000000\) | \([]\) | \(14112000\) | \(3.1259\) |
Rank
sage: E.rank()
The elliptic curves in class 157200bb have rank \(1\).
Complex multiplication
The elliptic curves in class 157200bb do not have complex multiplication.Modular form 157200.2.a.bb
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.