Properties

Label 46410.bz
Number of curves 44
Conductor 4641046410
CM no
Rank 11
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bz1")
 
E.isogeny_class()
 

Elliptic curves in class 46410.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46410.bz1 46410ca4 [1,0,0,73171,7584245][1, 0, 0, -73171, 7584245] 43325247696520145329/18353546828526043325247696520145329/183535468285260 183535468285260183535468285260 [2][2] 270336270336 1.59121.5912  
46410.bz2 46410ca2 [1,0,0,6871,13735][1, 0, 0, -6871, -13735] 35874636409222129/2068594131240035874636409222129/20685941312400 2068594131240020685941312400 [2,2][2, 2] 135168135168 1.24461.2446  
46410.bz3 46410ca1 [1,0,0,4871,130935][1, 0, 0, -4871, -130935] 12781554414694129/3638544000012781554414694129/36385440000 3638544000036385440000 [2][2] 6758467584 0.898020.89802 Γ0(N)\Gamma_0(N)-optimal
46410.bz4 46410ca3 [1,0,0,27429,102915][1, 0, 0, 27429, -102915] 2282194455855813071/13254954135204602282194455855813071/1325495413520460 1325495413520460-1325495413520460 [2][2] 270336270336 1.59121.5912  

Rank

sage: E.rank()
 

The elliptic curves in class 46410.bz have rank 11.

Complex multiplication

The elliptic curves in class 46410.bz do not have complex multiplication.

Modular form 46410.2.a.bz

sage: E.q_eigenform(10)
 
q+q2+q3+q4q5+q6q7+q8+q9q104q11+q12q13q14q15+q16q17+q18+4q19+O(q20)q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} - q^{7} + q^{8} + q^{9} - q^{10} - 4 q^{11} + q^{12} - q^{13} - q^{14} - q^{15} + q^{16} - q^{17} + q^{18} + 4 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.

(1244212242144241)\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.