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Properties

Label 158950dd
Number of curves $2$
Conductor $158950$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dd1")
 
E.isogeny_class()
 

Elliptic curves in class 158950dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158950.ba1 158950dd1 \([1, 0, 1, -7376, 665398]\) \(-117649/440\) \(-165945786875000\) \([]\) \(483840\) \(1.4142\) \(\Gamma_0(N)\)-optimal
158950.ba2 158950dd2 \([1, 0, 1, 64874, -15807602]\) \(80062991/332750\) \(-125496501324218750\) \([]\) \(1451520\) \(1.9635\)  

Rank

sage: E.rank()
 

The elliptic curves in class 158950dd have rank \(0\).

Complex multiplication

The elliptic curves in class 158950dd do not have complex multiplication.

Modular form 158950.2.a.dd

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.