Properties

Label 480.f
Number of curves $4$
Conductor $480$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 480.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
480.f1 480d2 \([0, 1, 0, -3601, -84385]\) \(1261112198464/675\) \(2764800\) \([2]\) \(384\) \(0.56564\)  
480.f2 480d3 \([0, 1, 0, -496, 2204]\) \(26410345352/10546875\) \(5400000000\) \([2]\) \(384\) \(0.56564\)  
480.f3 480d1 \([0, 1, 0, -226, -1360]\) \(20034997696/455625\) \(29160000\) \([2, 2]\) \(192\) \(0.21907\) \(\Gamma_0(N)\)-optimal
480.f4 480d4 \([0, 1, 0, 24, -3960]\) \(2863288/13286025\) \(-6802444800\) \([4]\) \(384\) \(0.56564\)  

Rank

sage: E.rank()
 

The elliptic curves in class 480.f have rank \(0\).

Complex multiplication

The elliptic curves in class 480.f do not have complex multiplication.

Modular form 480.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 4q^{7} + q^{9} - 4q^{11} + 6q^{13} - q^{15} + 2q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.