Properties

Label 270480.y
Number of curves $4$
Conductor $270480$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 270480.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270480.y1 270480y4 \([0, -1, 0, -139026736, -628674667760]\) \(2466780454987534385284/10072750481768625\) \(1213490197943907289728000\) \([2]\) \(53084160\) \(3.4771\)  
270480.y2 270480y2 \([0, -1, 0, -12974236, 881938240]\) \(8019382352783901136/4629798816890625\) \(139440947458141476000000\) \([2, 2]\) \(26542080\) \(3.1305\)  
270480.y3 270480y1 \([0, -1, 0, -9146111, 10622219490]\) \(44949507773962418176/132895751953125\) \(250160837144531250000\) \([2]\) \(13271040\) \(2.7839\) \(\Gamma_0(N)\)-optimal
270480.y4 270480y3 \([0, -1, 0, 51828264, 6999294240]\) \(127801365439147434716/74135664409456125\) \(-8931314464878698137728000\) \([2]\) \(53084160\) \(3.4771\)  

Rank

sage: E.rank()
 

The elliptic curves in class 270480.y have rank \(0\).

Complex multiplication

The elliptic curves in class 270480.y do not have complex multiplication.

Modular form 270480.2.a.y

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