Properties

Label 57800.n
Number of curves 4
Conductor 57800
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("57800.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 57800.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
57800.n1 57800s4 [0, 0, 0, -773075, -261617250] [2] 491520  
57800.n2 57800s2 [0, 0, 0, -50575, -3684750] [2, 2] 245760  
57800.n3 57800s1 [0, 0, 0, -14450, 614125] [2] 122880 \(\Gamma_0(N)\)-optimal
57800.n4 57800s3 [0, 0, 0, 93925, -20880250] [2] 491520  

Rank

sage: E.rank()
 

The elliptic curves in class 57800.n have rank \(0\).

Modular form 57800.2.a.n

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.