Properties

Label 950.b
Number of curves 22
Conductor 950950
CM no
Rank 11
Graph

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

Elliptic curves in class 950.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
950.b1 950a2 [1,0,1,1751,31352][1, 0, 1, -1751, -31352] 37966934881/4952198-37966934881/4952198 77378093750-77378093750 [][] 800800 0.822500.82250  
950.b2 950a1 [1,0,1,1,148][1, 0, 1, -1, 148] 1/608-1/608 9500000-9500000 [][] 160160 0.0177850.017785 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 950.b have rank 11.

Complex multiplication

The elliptic curves in class 950.b do not have complex multiplication.

Modular form 950.2.a.b

sage: E.q_eigenform(10)
 
qq2+q3+q4q63q7q82q9+2q11+q12+q13+3q14+q163q17+2q18q19+O(q20)q - q^{2} + q^{3} + q^{4} - q^{6} - 3 q^{7} - q^{8} - 2 q^{9} + 2 q^{11} + q^{12} + q^{13} + 3 q^{14} + q^{16} - 3 q^{17} + 2 q^{18} - q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the LMFDB numbering.

(1551)\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.