Properties

Label 272734.ce
Number of curves $2$
Conductor $272734$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("ce1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 272734.ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272734.ce1 272734ce2 \([1, 0, 0, -3590133, 2450930593]\) \(24553362849625/1755162752\) \(365815198215399244928\) \([2]\) \(13762560\) \(2.6927\)  
272734.ce2 272734ce1 \([1, 0, 0, 204427, 167364385]\) \(4533086375/60669952\) \(-12644975795725385728\) \([2]\) \(6881280\) \(2.3461\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 272734.ce have rank \(2\).

Complex multiplication

The elliptic curves in class 272734.ce do not have complex multiplication.

Modular form 272734.2.a.ce

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2q^{3} + q^{4} - 2q^{6} + q^{8} + q^{9} - 2q^{12} + q^{16} + 6q^{17} + q^{18} - 6q^{19} + O(q^{20})\)  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 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.