Properties

Label 270480.is
Number of curves $4$
Conductor $270480$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("is1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 270480.is

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270480.is1 270480is4 \([0, 1, 0, -2363492280, 120537971028]\) \(3029968325354577848895529/1753440696000000000000\) \(844966070041411584000000000000\) \([2]\) \(318504960\) \(4.4319\)  
270480.is2 270480is2 \([0, 1, 0, -1625893320, 25233322922100]\) \(986396822567235411402169/6336721794060000\) \(3053604791702998794240000\) \([2]\) \(106168320\) \(3.8826\)  
270480.is3 270480is1 \([0, 1, 0, -99664840, 410132431988]\) \(-227196402372228188089/19338934824115200\) \(-9319245181429060259020800\) \([2]\) \(53084160\) \(3.5360\) \(\Gamma_0(N)\)-optimal
270480.is4 270480is3 \([0, 1, 0, 590870600, 15362652500]\) \(47342661265381757089751/27397579603968000000\) \(-13202627964220339126272000000\) \([2]\) \(159252480\) \(4.0853\)  

Rank

sage: E.rank()
 

The elliptic curves in class 270480.is have rank \(1\).

Complex multiplication

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

Modular form 270480.2.a.is

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

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.