Properties

Label 104040.g
Number of curves $2$
Conductor $104040$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 104040.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
104040.g1 104040b2 \([0, 0, 0, -319923, 69243822]\) \(3721734/25\) \(24325108256102400\) \([2]\) \(983040\) \(1.9789\)  
104040.g2 104040b1 \([0, 0, 0, -7803, 2387718]\) \(-108/5\) \(-2432510825610240\) \([2]\) \(491520\) \(1.6323\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 104040.g have rank \(1\).

Complex multiplication

The elliptic curves in class 104040.g do not have complex multiplication.

Modular form 104040.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.