Properties

Label 9702.bl
Number of curves 22
Conductor 97029702
CM no
Rank 11
Graph

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 9702.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.bl1 9702bm2 [1,1,1,2573465,1589649401][1, -1, 1, -2573465, 1589649401] 448504189023625/135168-448504189023625/135168 568048917123072-568048917123072 [3][3] 145152145152 2.19532.1953  
9702.bl2 9702bm1 [1,1,1,26690,2906705][1, -1, 1, -26690, 2906705] 500313625/574992-500313625/574992 2416426838855568-2416426838855568 [][] 4838448384 1.64601.6460 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9702.bl have rank 11.

Complex multiplication

The elliptic curves in class 9702.bl do not have complex multiplication.

Modular form 9702.2.a.bl

sage: E.q_eigenform(10)
 
q+q2+q4+q8q114q13+q163q17q19+O(q20)q + q^{2} + q^{4} + q^{8} - q^{11} - 4 q^{13} + q^{16} - 3 q^{17} - 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.

(1331)\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.