Properties

Label 5520.bf
Number of curves $6$
Conductor $5520$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5520.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.bf1 5520k5 \([0, 1, 0, -870880, 301514900]\) \(35667215800077781442/1427217706746225\) \(2922941863416268800\) \([4]\) \(86016\) \(2.3097\)  
5520.bf2 5520k3 \([0, 1, 0, -141880, -14287900]\) \(308453964046598884/92949363050625\) \(95180147763840000\) \([2, 4]\) \(43008\) \(1.9631\)  
5520.bf3 5520k2 \([0, 1, 0, -129380, -17952900]\) \(935596404100595536/150641015625\) \(38564100000000\) \([2, 2]\) \(21504\) \(1.6165\)  
5520.bf4 5520k1 \([0, 1, 0, -129375, -17954352]\) \(14967807005098080256/388125\) \(6210000\) \([2]\) \(10752\) \(1.2699\) \(\Gamma_0(N)\)-optimal
5520.bf5 5520k4 \([0, 1, 0, -116960, -21524892]\) \(-172798332611391364/94757080078125\) \(-97031250000000000\) \([2]\) \(43008\) \(1.9631\)  
5520.bf6 5520k6 \([0, 1, 0, 387120, -95330700]\) \(3132776881711582558/3735130619961225\) \(-7649547509680588800\) \([4]\) \(86016\) \(2.3097\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5520.bf have rank \(0\).

Complex multiplication

The elliptic curves in class 5520.bf do not have complex multiplication.

Modular form 5520.2.a.bf

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + 4 q^{11} - 2 q^{13} + q^{15} + 2 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.