Properties

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

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 270802v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.v2 270802v1 \([1, 1, 1, 32361, -7960675]\) \(6300872423/49827568\) \(-29638599475113328\) \([2]\) \(2150400\) \(1.8421\) \(\Gamma_0(N)\)-optimal
270802.v1 270802v2 \([1, 1, 1, -455419, -108833579]\) \(17561807821657/1590616244\) \(946135636692626324\) \([2]\) \(4300800\) \(2.1887\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 270802.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} - 2 q^{5} + 2 q^{6} + q^{7} + q^{8} + q^{9} - 2 q^{10} + 2 q^{12} + 2 q^{13} + q^{14} - 4 q^{15} + q^{16} + q^{18} + 6 q^{19} + O(q^{20})\) Copy content 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.