Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 270802.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.o1 270802o2 \([1, -1, 1, -200316, 34450001]\) \(1494447319737/5411854\) \(3219096969047134\) \([2]\) \(2408448\) \(1.8367\)  
270802.o2 270802o1 \([1, -1, 1, -6886, 1025297]\) \(-60698457/725788\) \(-431715628501948\) \([2]\) \(1204224\) \(1.4901\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 270802.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 2q^{5} + q^{7} + q^{8} - 3q^{9} - 2q^{10} + 4q^{11} + 4q^{13} + q^{14} + q^{16} + 8q^{17} - 3q^{18} + 2q^{19} + O(q^{20})\)  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.