Properties

Label 381150.nj
Number of curves $2$
Conductor $381150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("nj1")
 
E.isogeny_class()
 

Elliptic curves in class 381150.nj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381150.nj1 381150nj1 \([1, -1, 1, -63303230, -193818967603]\) \(37537160298467283/5519360000\) \(4125044357280000000000\) \([2]\) \(41287680\) \(3.1618\) \(\Gamma_0(N)\)-optimal
381150.nj2 381150nj2 \([1, -1, 1, -57495230, -230827543603]\) \(-28124139978713043/14526050000000\) \(-10856439983271093750000000\) \([2]\) \(82575360\) \(3.5084\)  

Rank

sage: E.rank()
 

The elliptic curves in class 381150.nj have rank \(0\).

Complex multiplication

The elliptic curves in class 381150.nj do not have complex multiplication.

Modular form 381150.2.a.nj

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{7} + q^{8} - 4 q^{13} + q^{14} + q^{16} - 2 q^{17} + 6 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.