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Properties

Label 286286ba
Number of curves $2$
Conductor $286286$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 286286ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286286.ba2 286286ba1 \([1, 0, 1, 360, 1692]\) \(17303/14\) \(-4191513326\) \([]\) \(207360\) \(0.53420\) \(\Gamma_0(N)\)-optimal
286286.ba1 286286ba2 \([1, 0, 1, -7505, 253372]\) \(-156116857/2744\) \(-821536611896\) \([]\) \(622080\) \(1.0835\)  

Rank

sage: E.rank()
 

The elliptic curves in class 286286ba have rank \(1\).

Complex multiplication

The elliptic curves in class 286286ba do not have complex multiplication.

Modular form 286286.2.a.ba

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.