Properties

Label 7488.m
Number of curves $4$
Conductor $7488$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 7488.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7488.m1 7488r3 \([0, 0, 0, -134796, -19048624]\) \(11339065490696/351\) \(8384643072\) \([2]\) \(24576\) \(1.4086\)  
7488.m2 7488r2 \([0, 0, 0, -8436, -296800]\) \(22235451328/123201\) \(367876214784\) \([2, 2]\) \(12288\) \(1.0620\)  
7488.m3 7488r4 \([0, 0, 0, -3756, -624400]\) \(-245314376/6908733\) \(-165034929586176\) \([2]\) \(24576\) \(1.4086\)  
7488.m4 7488r1 \([0, 0, 0, -831, 1316]\) \(1360251712/771147\) \(35978634432\) \([2]\) \(6144\) \(0.71545\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7488.m have rank \(0\).

Complex multiplication

The elliptic curves in class 7488.m do not have complex multiplication.

Modular form 7488.2.a.m

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - 4 q^{11} - q^{13} + 6 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.