Properties

Label 428400.nu
Number of curves $6$
Conductor $428400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("428400.nu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 428400.nu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
428400.nu1 428400nu6 [0, 0, 0, -49386974475, -4224416420839750] [2] 754974720  
428400.nu2 428400nu4 [0, 0, 0, -3092558475, -65742737143750] [2, 2] 377487360  
428400.nu3 428400nu5 [0, 0, 0, -1053374475, -151145802247750] [2] 754974720  
428400.nu4 428400nu2 [0, 0, 0, -326606475, 570962056250] [2, 2] 188743680  
428400.nu5 428400nu1 [0, 0, 0, -252878475, 1545867400250] [2] 94371840 \(\Gamma_0(N)\)-optimal
428400.nu6 428400nu3 [0, 0, 0, 1259697525, 4490719240250] [2] 377487360  

Rank

sage: E.rank()
 

The elliptic curves in class 428400.nu have rank \(1\).

Modular form 428400.2.a.nu

sage: E.q_eigenform(10)
 
\( q + q^{7} + 4q^{11} + 2q^{13} + q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.