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Properties

Label 286650.lk
Number of curves $2$
Conductor $286650$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("lk1")
 
E.isogeny_class()
 

Elliptic curves in class 286650.lk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286650.lk1 286650lk2 \([1, -1, 1, -100305680, -356266408053]\) \(666276475992821/58199166792\) \(9749056213245808265625000\) \([2]\) \(70778880\) \(3.5355\)  
286650.lk2 286650lk1 \([1, -1, 1, -98100680, -373959328053]\) \(623295446073461/5458752\) \(914406219806625000000\) \([2]\) \(35389440\) \(3.1889\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 286650.lk have rank \(0\).

Complex multiplication

The elliptic curves in class 286650.lk do not have complex multiplication.

Modular form 286650.2.a.lk

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