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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 101150.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101150.bb1 | 101150r1 | \([1, 0, 1, -14659676, 21607432498]\) | \(-11060825617/2744\) | \(-86435738481750875000\) | \([]\) | \(5552064\) | \(2.8131\) | \(\Gamma_0(N)\)-optimal |
101150.bb2 | 101150r2 | \([1, 0, 1, 6220574, 76480729498]\) | \(845095823/80707214\) | \(-2542269549159877173218750\) | \([]\) | \(16656192\) | \(3.3624\) |
Rank
sage: E.rank()
The elliptic curves in class 101150.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 101150.bb do not have complex multiplication.Modular form 101150.2.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 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.