Properties

Label 1575f
Number of curves 4
Conductor 1575
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("1575.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1575f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1575.h3 1575f1 [1, -1, 0, -567, -4784] [2] 768 \(\Gamma_0(N)\)-optimal
1575.h2 1575f2 [1, -1, 0, -1692, 21091] [2, 2] 1536  
1575.h1 1575f3 [1, -1, 0, -25317, 1556716] [2] 3072  
1575.h4 1575f4 [1, -1, 0, 3933, 127966] [2] 3072  

Rank

sage: E.rank()
 

The elliptic curves in class 1575f have rank \(0\).

Modular form 1575.2.a.h

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - q^{7} - 3q^{8} + 6q^{13} - q^{14} - q^{16} + 2q^{17} - 8q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.