Properties

Label 102960.g
Number of curves $2$
Conductor $102960$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 102960.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102960.g1 102960cd2 \([0, 0, 0, -2027403, 1111113018]\) \(11431223764109163/148720\) \(11990039592960\) \([2]\) \(1474560\) \(2.0687\)  
102960.g2 102960cd1 \([0, 0, 0, -126603, 17392698]\) \(-2783584838763/10067200\) \(-811633449369600\) \([2]\) \(737280\) \(1.7221\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 102960.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.