Properties

Label 270802a
Number of curves $2$
Conductor $270802$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 270802a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.a2 270802a1 \([1, 0, 1, -7244392, -7404607710]\) \(70687311717054817/1093629002564\) \(650516035247035995044\) \([2]\) \(15052800\) \(2.7950\) \(\Gamma_0(N)\)-optimal
270802.a1 270802a2 \([1, 0, 1, -14317202, 9417363594]\) \(545644947830040577/251340262104722\) \(149503049406141189821762\) \([2]\) \(30105600\) \(3.1415\)  

Rank

sage: E.rank()
 

The elliptic curves in class 270802a have rank \(2\).

Complex multiplication

The elliptic curves in class 270802a do not have complex multiplication.

Modular form 270802.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2q^{3} + q^{4} - 2q^{5} + 2q^{6} - q^{7} - q^{8} + q^{9} + 2q^{10} - 2q^{11} - 2q^{12} - 4q^{13} + q^{14} + 4q^{15} + q^{16} - 2q^{17} - q^{18} + O(q^{20})\)  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.