Properties

Label 102960.j
Number of curves $4$
Conductor $102960$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 102960.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102960.j1 102960dy4 \([0, 0, 0, -11807643, -9439421942]\) \(60971359344939402841/22393337786551875\) \(66866148337239313920000\) \([4]\) \(11010048\) \(3.0800\)  
102960.j2 102960dy2 \([0, 0, 0, -10457643, -13013411942]\) \(42358217070122052841/12149581640625\) \(36278456385600000000\) \([2, 2]\) \(5505024\) \(2.7334\)  
102960.j3 102960dy1 \([0, 0, 0, -10456923, -13015293878]\) \(42349468688699229721/3485625\) \(10408020480000\) \([2]\) \(2752512\) \(2.3868\) \(\Gamma_0(N)\)-optimal
102960.j4 102960dy3 \([0, 0, 0, -9119163, -16466958038]\) \(-28086729490688202361/22976531982421875\) \(-68607556875000000000000\) \([2]\) \(11010048\) \(3.0800\)  

Rank

sage: E.rank()
 

The elliptic curves in class 102960.j have rank \(1\).

Complex multiplication

The elliptic curves in class 102960.j do not have complex multiplication.

Modular form 102960.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4 q^{7} + q^{11} + q^{13} - 6 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.