Properties

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

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Show commands: SageMath
E = EllipticCurve("jl1")
 
E.isogeny_class()
 

Elliptic curves in class 270480jl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270480.jl4 270480jl1 \([0, 1, 0, -18440, 64308]\) \(1439069689/828345\) \(399171423866880\) \([2]\) \(1081344\) \(1.4913\) \(\Gamma_0(N)\)-optimal
270480.jl2 270480jl2 \([0, 1, 0, -210520, 37020500]\) \(2141202151369/5832225\) \(2810492678246400\) \([2, 2]\) \(2162688\) \(1.8379\)  
270480.jl1 270480jl3 \([0, 1, 0, -3366120, 2375951220]\) \(8753151307882969/65205\) \(31421657272320\) \([4]\) \(4325376\) \(2.1844\)  
270480.jl3 270480jl4 \([0, 1, 0, -128200, 66359348]\) \(-483551781049/3672913125\) \(-1769941222371840000\) \([2]\) \(4325376\) \(2.1844\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 270480.2.a.jl

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