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Properties

Label 433698q
Number of curves $2$
Conductor $433698$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 433698q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
433698.q2 433698q1 \([1, 1, 1, 267244, 118914005]\) \(444369620591/1540767744\) \(-7318807395170402304\) \([]\) \(11854080\) \(2.3028\) \(\Gamma_0(N)\)-optimal
433698.q1 433698q2 \([1, 1, 1, -100693616, -388999772875]\) \(-23769846831649063249/3261823333284\) \(-15494000848825084857444\) \([]\) \(82978560\) \(3.2757\)  

Rank

sage: E.rank()
 

The elliptic curves in class 433698q have rank \(1\).

Complex multiplication

The elliptic curves in class 433698q do not have complex multiplication.

Modular form 433698.2.a.q

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