Properties

Label 211420.n
Number of curves 4
Conductor 211420
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("211420.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 211420.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
211420.n1 211420m4 [0, -1, 0, -6823420, 6862702632] [2] 6220800  
211420.n2 211420m3 [0, -1, 0, -427965, 106543970] [2] 3110400  
211420.n3 211420m2 [0, -1, 0, -96420, 6544232] [2] 2073600  
211420.n4 211420m1 [0, -1, 0, -43565, -3413650] [2] 1036800 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 211420.n have rank \(1\).

Modular form 211420.2.a.n

sage: E.q_eigenform(10)
 
\( q + 2q^{3} + q^{5} - 4q^{7} + q^{9} + q^{11} + 4q^{13} + 2q^{15} - 4q^{19} + O(q^{20}) \)

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.