Properties

Label 203840t
Number of curves $2$
Conductor $203840$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 203840t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
203840.z1 203840t1 \([0, 1, 0, -93361, 10125135]\) \(46689225424/3901625\) \(7520621029376000\) \([2]\) \(1769472\) \(1.7883\) \(\Gamma_0(N)\)-optimal
203840.z2 203840t2 \([0, 1, 0, 98719, 46581919]\) \(13799183324/129390625\) \(-997633401856000000\) \([2]\) \(3538944\) \(2.1349\)  

Rank

sage: E.rank()
 

The elliptic curves in class 203840t have rank \(1\).

Complex multiplication

The elliptic curves in class 203840t do not have complex multiplication.

Modular form 203840.2.a.t

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} + q^{9} + 6 q^{11} - q^{13} + 2 q^{15} + 2 q^{17} - 2 q^{19} + O(q^{20})\) 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 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.