Properties

Label 102960.d
Number of curves $4$
Conductor $102960$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 102960.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102960.d1 102960y4 \([0, 0, 0, -1460523, -679376662]\) \(461552841274085284/111344805\) \(83118451553280\) \([2]\) \(1179648\) \(2.0486\)  
102960.d2 102960y3 \([0, 0, 0, -180723, 13293218]\) \(874453074310084/403786706895\) \(301425161550289920\) \([2]\) \(1179648\) \(2.0486\)  
102960.d3 102960y2 \([0, 0, 0, -91623, -10532122]\) \(455795194086736/6998159025\) \(1306024429881600\) \([2, 2]\) \(589824\) \(1.7021\)  
102960.d4 102960y1 \([0, 0, 0, -498, -453697]\) \(-1171019776/7623061875\) \(-88915393710000\) \([2]\) \(294912\) \(1.3555\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 102960.d have rank \(0\).

Complex multiplication

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

Modular form 102960.2.a.d

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