Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 480.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
480.d1 480b2 \([0, -1, 0, -160, -728]\) \(890277128/15\) \(7680\) \([2]\) \(64\) \(-0.12420\)  
480.d2 480b3 \([0, -1, 0, -40, 100]\) \(14172488/1875\) \(960000\) \([4]\) \(64\) \(-0.12420\)  
480.d3 480b1 \([0, -1, 0, -10, -8]\) \(1906624/225\) \(14400\) \([2, 2]\) \(32\) \(-0.47077\) \(\Gamma_0(N)\)-optimal
480.d4 480b4 \([0, -1, 0, 15, -63]\) \(85184/405\) \(-1658880\) \([2]\) \(64\) \(-0.12420\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 480.2.a.d

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