Properties

Label 227850.bi
Number of curves $2$
Conductor $227850$
CM no
Rank $1$
Graph

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

Elliptic curves in class 227850.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
227850.bi1 227850iy2 \([1, 1, 0, -809750, 280125000]\) \(31942518433489/27900\) \(51287610937500\) \([2]\) \(2764800\) \(1.9311\)  
227850.bi2 227850iy1 \([1, 1, 0, -50250, 4426500]\) \(-7633736209/230640\) \(-423977583750000\) \([2]\) \(1382400\) \(1.5845\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 227850.bi have rank \(1\).

Complex multiplication

The elliptic curves in class 227850.bi do not have complex multiplication.

Modular form 227850.2.a.bi

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - q^{12} + 4 q^{13} + q^{16} + 6 q^{17} - q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.