Properties

Label 176400.lf
Number of curves $4$
Conductor $176400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("176400.lf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 176400.lf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.lf1 176400kd3 [0, 0, 0, -8235675, -7971405750] [2] 7962624  
176400.lf2 176400kd1 [0, 0, 0, -2061675, 1137988250] [2] 2654208 \(\Gamma_0(N)\)-optimal
176400.lf3 176400kd2 [0, 0, 0, -1473675, 1800664250] [2] 5308416  
176400.lf4 176400kd4 [0, 0, 0, 12932325, -42200061750] [2] 15925248  

Rank

sage: E.rank()
 

The elliptic curves in class 176400.lf have rank \(1\).

Modular form 176400.2.a.lf

sage: E.q_eigenform(10)
 
\( q + 2q^{13} + 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.