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Properties

Label 7488g
Number of curves $2$
Conductor $7488$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 7488g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7488.r2 7488g1 \([0, 0, 0, 324, -2160]\) \(11664/13\) \(-4192321536\) \([2]\) \(3072\) \(0.53286\) \(\Gamma_0(N)\)-optimal
7488.r1 7488g2 \([0, 0, 0, -1836, -20304]\) \(530604/169\) \(218000719872\) \([2]\) \(6144\) \(0.87944\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7488.2.a.g

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + 2 q^{7} - 4 q^{11} + q^{13} + 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.