Properties

Label 360.b
Number of curves $6$
Conductor $360$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 360.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
360.b1 360a5 \([0, 0, 0, -28803, 1881502]\) \(1770025017602/75\) \(111974400\) \([2]\) \(512\) \(1.0293\)  
360.b2 360a3 \([0, 0, 0, -1803, 29302]\) \(868327204/5625\) \(4199040000\) \([2, 2]\) \(256\) \(0.68273\)  
360.b3 360a6 \([0, 0, 0, -723, 64078]\) \(-27995042/1171875\) \(-1749600000000\) \([2]\) \(512\) \(1.0293\)  
360.b4 360a2 \([0, 0, 0, -183, -182]\) \(3631696/2025\) \(377913600\) \([2, 2]\) \(128\) \(0.33616\)  
360.b5 360a1 \([0, 0, 0, -138, -623]\) \(24918016/45\) \(524880\) \([2]\) \(64\) \(-0.010416\) \(\Gamma_0(N)\)-optimal
360.b6 360a4 \([0, 0, 0, 717, -1442]\) \(54607676/32805\) \(-24488801280\) \([2]\) \(256\) \(0.68273\)  

Rank

sage: E.rank()
 

The elliptic curves in class 360.b have rank \(0\).

Complex multiplication

The elliptic curves in class 360.b do not have complex multiplication.

Modular form 360.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4q^{11} + 6q^{13} + 6q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.