Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7488.cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7488.cc1 7488cc1 \([0, 0, 0, -23448, 1298360]\) \(1909913257984/129730653\) \(96843413541888\) \([2]\) \(30720\) \(1.4323\) \(\Gamma_0(N)\)-optimal
7488.cc2 7488cc2 \([0, 0, 0, 20292, 5584880]\) \(77366117936/1172914587\) \(-14009216760594432\) \([2]\) \(61440\) \(1.7788\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7488.2.a.cc

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.