Properties

Label 102960di
Number of curves $4$
Conductor $102960$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("di1")
 
E.isogeny_class()
 

Elliptic curves in class 102960di

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102960.o4 102960di1 \([0, 0, 0, -86043, -111791158]\) \(-23592983745241/1794399750000\) \(-5358048943104000000\) \([2]\) \(1327104\) \(2.2734\) \(\Gamma_0(N)\)-optimal
102960.o3 102960di2 \([0, 0, 0, -4046043, -3111095158]\) \(2453170411237305241/19353090685500\) \(57788019137452032000\) \([2]\) \(2654208\) \(2.6200\)  
102960.o2 102960di3 \([0, 0, 0, -20444043, -35580060358]\) \(-316472948332146183241/7074906009600\) \(-21125556146169446400\) \([2]\) \(3981312\) \(2.8228\)  
102960.o1 102960di4 \([0, 0, 0, -327106443, -2277098206918]\) \(1296294060988412126189641/647824320\) \(1934393054330880\) \([2]\) \(7962624\) \(3.1693\)  

Rank

sage: E.rank()
 

The elliptic curves in class 102960di have rank \(2\).

Complex multiplication

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

Modular form 102960.2.a.di

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2 q^{7} - q^{11} + q^{13} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.