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Properties

Label 11550.bi
Number of curves $2$
Conductor $11550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 11550.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11550.bi1 11550bi1 \([1, 0, 1, -2076, 174298]\) \(-2531307865/32199552\) \(-12577950000000\) \([3]\) \(30240\) \(1.1953\) \(\Gamma_0(N)\)-optimal
11550.bi2 11550bi2 \([1, 0, 1, 18549, -4528202]\) \(1807002849335/23737663488\) \(-9272524800000000\) \([]\) \(90720\) \(1.7446\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11550.bi have rank \(1\).

Complex multiplication

The elliptic curves in class 11550.bi do not have complex multiplication.

Modular form 11550.2.a.bi

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + q^{7} - q^{8} + q^{9} + q^{11} + q^{12} - 4 q^{13} - q^{14} + q^{16} - q^{18} + 2 q^{19} + O(q^{20})\) 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.