Properties

Label 102960.i
Number of curves $2$
Conductor $102960$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 102960.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102960.i1 102960dl2 \([0, 0, 0, -15843, -499358]\) \(147281603041/49156250\) \(146779776000000\) \([2]\) \(331776\) \(1.4209\)  
102960.i2 102960dl1 \([0, 0, 0, 2877, -53822]\) \(881974079/929500\) \(-2775472128000\) \([2]\) \(165888\) \(1.0744\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 102960.2.a.i

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.