Properties

Label 2475g
Number of curves 4
Conductor 2475
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("2475.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2475g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2475.g3 2475g1 [1, -1, 0, -1467, 21816] [2] 1536 \(\Gamma_0(N)\)-optimal
2475.g2 2475g2 [1, -1, 0, -2592, -15309] [2, 2] 3072  
2475.g1 2475g3 [1, -1, 0, -32967, -2293434] [2] 6144  
2475.g4 2475g4 [1, -1, 0, 9783, -126684] [2] 6144  

Rank

sage: E.rank()
 

The elliptic curves in class 2475g have rank \(0\).

Modular form 2475.2.a.g

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - 4q^{7} - 3q^{8} - q^{11} + 2q^{13} - 4q^{14} - q^{16} - 2q^{17} + O(q^{20}) \)

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.