Properties

Label 388542.n
Number of curves $4$
Conductor $388542$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 388542.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388542.n1 388542n4 \([1, 1, 0, -11885870, -15776129754]\) \(312196988566716625/25367712678\) \(15089307101301763638\) \([2]\) \(13934592\) \(2.7252\)  
388542.n2 388542n3 \([1, 1, 0, -692160, -281796372]\) \(-61653281712625/21875235228\) \(-13011900065975152188\) \([2]\) \(6967296\) \(2.3786\)  
388542.n3 388542n2 \([1, 1, 0, -305300, 32438232]\) \(5290763640625/2291573592\) \(1363081414309339032\) \([2]\) \(4644864\) \(2.1759\)  
388542.n4 388542n1 \([1, 1, 0, 64740, 3797136]\) \(50447927375/39517632\) \(-23506009104295872\) \([2]\) \(2322432\) \(1.8293\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 388542.n have rank \(1\).

Complex multiplication

The elliptic curves in class 388542.n do not have complex multiplication.

Modular form 388542.2.a.n

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.