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Properties

Label 249090dj
Number of curves $2$
Conductor $249090$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dj1")
 
E.isogeny_class()
 

Elliptic curves in class 249090dj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
249090.dj2 249090dj1 \([1, 0, 0, -8222685, 623088491697]\) \(-1306902141891515161/3564268498800000000\) \(-167684151646593442800000000\) \([2]\) \(104509440\) \(3.7110\) \(\Gamma_0(N)\)-optimal
249090.dj1 249090dj2 \([1, 0, 0, -1145112765, 14728028958225]\) \(3529773792266261468365081/50841342773437500000\) \(2391875761999350585937500000\) \([2]\) \(209018880\) \(4.0575\)  

Rank

sage: E.rank()
 

The elliptic curves in class 249090dj have rank \(1\).

Complex multiplication

The elliptic curves in class 249090dj do not have complex multiplication.

Modular form 249090.2.a.dj

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