Properties

Label 1960k
Number of curves $2$
Conductor $1960$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1960k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1960.b2 1960k1 \([0, 1, 0, 1944, -35456]\) \(19652/25\) \(-1033052339200\) \([2]\) \(2688\) \(0.99128\) \(\Gamma_0(N)\)-optimal
1960.b1 1960k2 \([0, 1, 0, -11776, -353760]\) \(2185454/625\) \(51652616960000\) \([2]\) \(5376\) \(1.3379\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1960k have rank \(1\).

Complex multiplication

The elliptic curves in class 1960k do not have complex multiplication.

Modular form 1960.2.a.k

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} + q^{9} + 4 q^{11} - 2 q^{13} + 2 q^{15} - 2 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.