Properties

Label 855.a
Number of curves $4$
Conductor $855$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 855.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
855.a1 855a4 \([1, -1, 1, -54068, 4852482]\) \(23977812996389881/146611125\) \(106879510125\) \([2]\) \(2304\) \(1.3034\)  
855.a2 855a3 \([1, -1, 1, -11138, -363594]\) \(209595169258201/41748046875\) \(30434326171875\) \([2]\) \(2304\) \(1.3034\)  
855.a3 855a2 \([1, -1, 1, -3443, 73482]\) \(6189976379881/456890625\) \(333073265625\) \([2, 2]\) \(1152\) \(0.95687\)  
855.a4 855a1 \([1, -1, 1, 202, 4956]\) \(1256216039/15582375\) \(-11359551375\) \([2]\) \(576\) \(0.61030\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 855.a have rank \(0\).

Complex multiplication

The elliptic curves in class 855.a do not have complex multiplication.

Modular form 855.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} + 4 q^{7} + 3 q^{8} + q^{10} - 4 q^{11} + 2 q^{13} - 4 q^{14} - q^{16} - 2 q^{17} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.