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Properties

Label 270802p
Number of curves $2$
Conductor $270802$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 270802p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.p2 270802p1 \([1, -1, 1, 48620, 340723]\) \(21369234375/12456892\) \(-7409649868778332\) \([2]\) \(1397760\) \(1.7346\) \(\Gamma_0(N)\)-optimal
270802.p1 270802p2 \([1, -1, 1, -195270, 2877179]\) \(1384331873625/795308122\) \(473067818346313162\) \([2]\) \(2795520\) \(2.0811\)  

Rank

sage: E.rank()
 

The elliptic curves in class 270802p have rank \(1\).

Complex multiplication

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

Modular form 270802.2.a.p

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