Properties

Label 6960.bd
Number of curves 22
Conductor 69606960
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 6960.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6960.bd1 6960bi2 [0,1,0,2096,36180][0, 1, 0, -2096, 36180] 248739515569/504600248739515569/504600 20668416002066841600 [2][2] 46084608 0.674170.67417  
6960.bd2 6960bi1 [0,1,0,176,84][0, 1, 0, -176, 84] 148035889/83520148035889/83520 342097920342097920 [2][2] 23042304 0.327590.32759 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6960.bd have rank 00.

Complex multiplication

The elliptic curves in class 6960.bd do not have complex multiplication.

Modular form 6960.2.a.bd

sage: E.q_eigenform(10)
 
q+q3q5+2q7+q9+2q11q152q17+8q19+O(q20)q + q^{3} - q^{5} + 2 q^{7} + q^{9} + 2 q^{11} - q^{15} - 2 q^{17} + 8 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.

(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 LMFDB labels.