Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 270802.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.e1 270802e2 \([1, -1, 0, -336033061, -2272124875275]\) \(7054751972146948898193/332947845138448288\) \(198045142965045515454924448\) \([2]\) \(90316800\) \(3.8066\)  
270802.e2 270802e1 \([1, -1, 0, -332130821, -2329675891243]\) \(6811821555839776164753/16312107262976\) \(9702821814671604663296\) \([2]\) \(45158400\) \(3.4600\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 270802.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2q^{5} - q^{7} - q^{8} - 3q^{9} - 2q^{10} - 4q^{11} + q^{14} + q^{16} + 6q^{17} + 3q^{18} - 4q^{19} + O(q^{20})\)  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.