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Properties

Label 57150.bb
Number of curves $2$
Conductor $57150$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 57150.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57150.bb1 57150bi2 \([1, -1, 1, -125930, -2018303]\) \(28724783355/16387064\) \(125994758090625000\) \([]\) \(699840\) \(1.9710\)  
57150.bb2 57150bi1 \([1, -1, 1, -80930, 8881697]\) \(5558063491395/65024\) \(685800000000\) \([3]\) \(233280\) \(1.4217\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 57150.bb have rank \(2\).

Complex multiplication

The elliptic curves in class 57150.bb do not have complex multiplication.

Modular form 57150.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 4 q^{7} + q^{8} - 3 q^{11} - 4 q^{13} - 4 q^{14} + q^{16} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.