Properties

Label 156.b
Number of curves $4$
Conductor $156$
CM no
Rank $0$
Graph

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

Elliptic curves in class 156.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
156.b1 156b4 \([0, 1, 0, -748, -7564]\) \(181037698000/14480427\) \(3706989312\) \([2]\) \(72\) \(0.57946\)  
156.b2 156b3 \([0, 1, 0, -733, -7888]\) \(2725888000000/19773\) \(316368\) \([2]\) \(36\) \(0.23288\)  
156.b3 156b2 \([0, 1, 0, -148, 644]\) \(1409938000/4563\) \(1168128\) \([6]\) \(24\) \(0.030152\)  
156.b4 156b1 \([0, 1, 0, -13, -4]\) \(16384000/9477\) \(151632\) \([6]\) \(12\) \(-0.31642\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 156.b have rank \(0\).

Complex multiplication

The elliptic curves in class 156.b do not have complex multiplication.

Modular form 156.2.a.b

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.