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Properties

Label 234.b
Number of curves $2$
Conductor $234$
CM no
Rank $0$
Graph

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

Elliptic curves in class 234.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
234.b1 234a2 \([1, -1, 0, -1914, 35846]\) \(-1064019559329/125497034\) \(-91487337786\) \([]\) \(196\) \(0.83910\)  
234.b2 234a1 \([1, -1, 0, -24, -64]\) \(-2146689/1664\) \(-1213056\) \([]\) \(28\) \(-0.13385\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 234.b have rank \(0\).

Complex multiplication

The elliptic curves in class 234.b do not have complex multiplication.

Modular form 234.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} + 2 q^{11} - q^{13} - q^{14} + q^{16} + 3 q^{17} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.