Properties

Label 23104.bj
Number of curves 33
Conductor 2310423104
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 23104.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23104.bj1 23104l3 [0,1,0,1975873,8598438175][0, 1, 0, -1975873, 8598438175] 69173457625/2550136832-69173457625/2550136832 31450315864667322318848-31450315864667322318848 [][] 12441601244160 2.99712.9971  
23104.bj2 23104l1 [0,1,0,358593,82797409][0, 1, 0, -358593, -82797409] 413493625/152-413493625/152 1874584905187328-1874584905187328 [][] 138240138240 1.89851.8985 Γ0(N)\Gamma_0(N)-optimal
23104.bj3 23104l2 [0,1,0,219007,314091553][0, 1, 0, 219007, -314091553] 94196375/351180894196375/3511808 43310409649448026112-43310409649448026112 [][] 414720414720 2.44782.4478  

Rank

sage: E.rank()
 

The elliptic curves in class 23104.bj have rank 00.

Complex multiplication

The elliptic curves in class 23104.bj do not have complex multiplication.

Modular form 23104.2.a.bj

sage: E.q_eigenform(10)
 
q+q3q72q9+6q11+5q13+3q17+O(q20)q + q^{3} - q^{7} - 2 q^{9} + 6 q^{11} + 5 q^{13} + 3 q^{17} + 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.

(193913331)\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.