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Properties

Label 214774.n
Number of curves $2$
Conductor $214774$
CM no
Rank $1$
Graph

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

Elliptic curves in class 214774.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
214774.n1 214774d2 \([1, -1, 1, -211369191, 1133595237887]\) \(7054751972146948898193/332947845138448288\) \(49288230245704520394608032\) \([2]\) \(56770560\) \(3.6907\)  
214774.n2 214774d1 \([1, -1, 1, -208914631, 1162304753471]\) \(6811821555839776164753/16312107262976\) \(2414777300138008945664\) \([2]\) \(28385280\) \(3.3441\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 214774.n have rank \(1\).

Complex multiplication

The elliptic curves in class 214774.n do not have complex multiplication.

Modular form 214774.2.a.n

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