Properties

Label 62160db
Number of curves $4$
Conductor $62160$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("db1")
 
E.isogeny_class()
 

Elliptic curves in class 62160db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62160.cz4 62160db1 \([0, 1, 0, 1280, -13900]\) \(56578878719/54390000\) \(-222781440000\) \([2]\) \(61440\) \(0.86454\) \(\Gamma_0(N)\)-optimal
62160.cz3 62160db2 \([0, 1, 0, -6720, -132300]\) \(8194759433281/2958272100\) \(12117082521600\) \([2, 2]\) \(122880\) \(1.2111\)  
62160.cz2 62160db3 \([0, 1, 0, -45920, 3677940]\) \(2614441086442081/74385450090\) \(304682803568640\) \([4]\) \(245760\) \(1.5577\)  
62160.cz1 62160db4 \([0, 1, 0, -95520, -11392140]\) \(23531588875176481/6398929110\) \(26210013634560\) \([2]\) \(245760\) \(1.5577\)  

Rank

sage: E.rank()
 

The elliptic curves in class 62160db have rank \(0\).

Complex multiplication

The elliptic curves in class 62160db do not have complex multiplication.

Modular form 62160.2.a.db

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{7} + q^{9} - 2 q^{13} + q^{15} + 2 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.