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Properties

Label 88270u
Number of curves $2$
Conductor $88270$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 88270u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88270.k2 88270u1 \([1, -1, 1, 2810783433, 57129831452559]\) \(2455872791358451393794120395694399/2831226586844364800000000000000\) \(-2831226586844364800000000000000\) \([7]\) \(285815040\) \(4.5295\) \(\Gamma_0(N)\)-optimal
88270.k1 88270u2 \([1, -1, 1, -938726820567, -350077314766040241]\) \(-91483209224241436429962941197655681681601/1781546240931158951849152905279200\) \(-1781546240931158951849152905279200\) \([]\) \(2000705280\) \(5.5025\)  

Rank

sage: E.rank()
 

The elliptic curves in class 88270u have rank \(0\).

Complex multiplication

The elliptic curves in class 88270u do not have complex multiplication.

Modular form 88270.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} + q^{5} - 3 q^{6} + q^{7} + q^{8} + 6 q^{9} + q^{10} - 2 q^{11} - 3 q^{12} - q^{13} + q^{14} - 3 q^{15} + q^{16} - 3 q^{17} + 6 q^{18} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.