Properties

Label 75504.j
Number of curves $6$
Conductor $75504$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("75504.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75504.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
75504.j1 75504bj4 [0, -1, 0, -13288744, 18649929520] [2] 1966080  
75504.j2 75504bj6 [0, -1, 0, -5825464, -5238513872] [2] 3932160  
75504.j3 75504bj3 [0, -1, 0, -917704, 226767664] [2, 2] 1966080  
75504.j4 75504bj2 [0, -1, 0, -830584, 291584944] [2, 2] 983040  
75504.j5 75504bj1 [0, -1, 0, -46504, 5552560] [2] 491520 \(\Gamma_0(N)\)-optimal
75504.j6 75504bj5 [0, -1, 0, 2596136, 1542349360] [2] 3932160  

Rank

sage: E.rank()
 

The elliptic curves in class 75504.j have rank \(1\).

Modular form 75504.2.a.j

sage: E.q_eigenform(10)
 
\( q - q^{3} - 2q^{5} + q^{9} - q^{13} + 2q^{15} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.