Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 7488.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7488.t1 7488s3 \([0, 0, 0, -10956, 430576]\) \(3044193988/85293\) \(4074936532992\) \([2]\) \(16384\) \(1.1987\)  
7488.t2 7488s2 \([0, 0, 0, -1596, -14960]\) \(37642192/13689\) \(163500539904\) \([2, 2]\) \(8192\) \(0.85214\)  
7488.t3 7488s1 \([0, 0, 0, -1416, -20504]\) \(420616192/117\) \(87340032\) \([2]\) \(4096\) \(0.50557\) \(\Gamma_0(N)\)-optimal
7488.t4 7488s4 \([0, 0, 0, 4884, -105680]\) \(269676572/257049\) \(-12280707219456\) \([2]\) \(16384\) \(1.1987\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7488.2.a.t

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + 4 q^{7} - q^{13} - 2 q^{17} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.