↑

Properties

Label 154.b
Number of curves $2$
Conductor $154$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 154.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154.b1 154c2 \([1, 1, 0, -234, -1480]\) \(1426487591593/2156\) \(2156\) \([2]\) \(32\) \(-0.092314\)  
154.b2 154c1 \([1, 1, 0, -14, -28]\) \(-338608873/13552\) \(-13552\) \([2]\) \(16\) \(-0.43889\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 154.b have rank \(0\).

Complex multiplication

The elliptic curves in class 154.b do not have complex multiplication.

Modular form 154.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} + 2 q^{5} - 2 q^{6} - q^{7} - q^{8} + q^{9} - 2 q^{10} + q^{11} + 2 q^{12} - 4 q^{13} + q^{14} + 4 q^{15} + q^{16} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.