Properties

Label 367575bl
Number of curves 22
Conductor 367575367575
CM no
Rank 11
Graph

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

Elliptic curves in class 367575bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
367575.bl2 367575bl1 [1,1,0,3045,28800][1, 1, 0, -3045, 28800] 5177717/23495177717/2349 14172717926251417271792625 [2][2] 414720414720 1.02681.0268 Γ0(N)\Gamma_0(N)-optimal
367575.bl1 367575bl2 [1,1,0,41070,3184875][1, 1, 0, -41070, 3184875] 12698260037/756912698260037/7569 45667646651254566764665125 [2][2] 829440829440 1.37331.3733  

Rank

sage: E.rank()
 

The elliptic curves in class 367575bl have rank 11.

Complex multiplication

The elliptic curves in class 367575bl do not have complex multiplication.

Modular form 367575.2.a.bl

sage: E.q_eigenform(10)
 
q+q2q3q4q62q73q8+q9+q122q14q162q17+q18+O(q20)q + q^{2} - q^{3} - q^{4} - q^{6} - 2 q^{7} - 3 q^{8} + q^{9} + q^{12} - 2 q^{14} - q^{16} - 2 q^{17} + q^{18} + 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 Cremona numbering.

(1221)\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with Cremona labels.