Properties

Label 270802j
Number of curves $2$
Conductor $270802$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 270802j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.j2 270802j1 \([1, 1, 0, 77355, -154723]\) \(86058173375/49827568\) \(-29638599475113328\) \([2]\) \(2257920\) \(1.8501\) \(\Gamma_0(N)\)-optimal
270802.j1 270802j2 \([1, 1, 0, -309505, -1624791]\) \(5512402554625/3188422748\) \(1896548207717306108\) \([2]\) \(4515840\) \(2.1967\)  

Rank

sage: E.rank()
 

The elliptic curves in class 270802j have rank \(0\).

Complex multiplication

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

Modular form 270802.2.a.j

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