Properties

Label 850.b
Number of curves $2$
Conductor $850$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 850.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
850.b1 850a2 \([1, 1, 0, -166025, -26946875]\) \(-32391289681150609/1228250000000\) \(-19191406250000000\) \([]\) \(6048\) \(1.8945\)  
850.b2 850a1 \([1, 1, 0, 9975, -114875]\) \(7023836099951/4456448000\) \(-69632000000000\) \([]\) \(2016\) \(1.3452\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 850.b have rank \(0\).

Complex multiplication

The elliptic curves in class 850.b do not have complex multiplication.

Modular form 850.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 2 q^{7} - q^{8} - 2 q^{9} - q^{12} + q^{13} + 2 q^{14} + q^{16} + q^{17} + 2 q^{18} - q^{19} + O(q^{20})\) 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.