Properties

Label 155526bf
Number of curves $4$
Conductor $155526$
CM no
Rank $0$
Graph

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

Elliptic curves in class 155526bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155526.bu4 155526bf1 \([1, 1, 1, -15527219, -38421864223]\) \(-23771111713777/22848457968\) \(-397935011416059822379248\) \([2]\) \(24330240\) \(3.2245\) \(\Gamma_0(N)\)-optimal
155526.bu3 155526bf2 \([1, 1, 1, -289771399, -1898126497639]\) \(154502321244119857/55101928644\) \(959670303996291717202884\) \([2, 2]\) \(48660480\) \(3.5711\)  
155526.bu2 155526bf3 \([1, 1, 1, -331504209, -1315720094403]\) \(231331938231569617/90942310746882\) \(1583876229894699585347881602\) \([2]\) \(97320960\) \(3.9177\)  
155526.bu1 155526bf4 \([1, 1, 1, -4635945469, -121496144555899]\) \(632678989847546725777/80515134\) \(1402273659444691779774\) \([2]\) \(97320960\) \(3.9177\)  

Rank

sage: E.rank()
 

The elliptic curves in class 155526bf have rank \(0\).

Complex multiplication

The elliptic curves in class 155526bf do not have complex multiplication.

Modular form 155526.2.a.bf

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{8} + q^{9} - 2 q^{10} - 4 q^{11} - q^{12} - 2 q^{13} + 2 q^{15} + q^{16} + 6 q^{17} + q^{18} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.