Properties

Label 32400.g
Number of curves 22
Conductor 3240032400
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 32400.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32400.g1 32400by1 [0,0,0,2475,51750][0, 0, 0, -2475, -51750] 35937/4-35937/4 186624000000-186624000000 [][] 3110431104 0.900060.90006 Γ0(N)\Gamma_0(N)-optimal
32400.g2 32400by2 [0,0,0,15525,74250][0, 0, 0, 15525, 74250] 109503/64109503/64 241864704000000-241864704000000 [][] 9331293312 1.44941.4494  

Rank

sage: E.rank()
 

The elliptic curves in class 32400.g have rank 00.

Complex multiplication

The elliptic curves in class 32400.g do not have complex multiplication.

Modular form 32400.2.a.g

sage: E.q_eigenform(10)
 
q4q7+q13+3q17+4q19+O(q20)q - 4 q^{7} + q^{13} + 3 q^{17} + 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.

(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.