Properties

Label 960b
Number of curves $6$
Conductor $960$
CM no
Rank $1$
Graph

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

Elliptic curves in class 960b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
960.c5 960b1 \([0, -1, 0, -61, 205]\) \(24918016/45\) \(46080\) \([2]\) \(128\) \(-0.21315\) \(\Gamma_0(N)\)-optimal
960.c4 960b2 \([0, -1, 0, -81, 81]\) \(3631696/2025\) \(33177600\) \([2, 2]\) \(256\) \(0.13343\)  
960.c2 960b3 \([0, -1, 0, -801, -8415]\) \(868327204/5625\) \(368640000\) \([2, 2]\) \(512\) \(0.48000\)  
960.c6 960b4 \([0, -1, 0, 319, 321]\) \(54607676/32805\) \(-2149908480\) \([2]\) \(512\) \(0.48000\)  
960.c1 960b5 \([0, -1, 0, -12801, -553215]\) \(1770025017602/75\) \(9830400\) \([2]\) \(1024\) \(0.82657\)  
960.c3 960b6 \([0, -1, 0, -321, -18879]\) \(-27995042/1171875\) \(-153600000000\) \([2]\) \(1024\) \(0.82657\)  

Rank

sage: E.rank()
 

The elliptic curves in class 960b have rank \(1\).

Complex multiplication

The elliptic curves in class 960b do not have complex multiplication.

Modular form 960.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} + 4 q^{11} - 6 q^{13} + q^{15} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.