Properties

Label 271440k
Number of curves $2$
Conductor $271440$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 271440k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
271440.k2 271440k1 \([0, 0, 0, -14283, 1781882]\) \(-2913790403187/10716526600\) \(-1185162109747200\) \([]\) \(1078272\) \(1.5781\) \(\Gamma_0(N)\)-optimal
271440.k1 271440k2 \([0, 0, 0, -1642923, 810540378]\) \(-6083088015781323/11781250\) \(-949822848000000\) \([]\) \(3234816\) \(2.1274\)  

Rank

sage: E.rank()
 

The elliptic curves in class 271440k have rank \(2\).

Complex multiplication

The elliptic curves in class 271440k do not have complex multiplication.

Modular form 271440.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2 q^{7} - 3 q^{11} + q^{13} - 3 q^{17} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.