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Properties

Label 3570.j
Number of curves $4$
Conductor $3570$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 3570.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3570.j1 3570j4 \([1, 0, 1, -15284, -722854]\) \(394815279796185529/3548222643000\) \(3548222643000\) \([2]\) \(13824\) \(1.2309\)  
3570.j2 3570j2 \([1, 0, 1, -1319, 17732]\) \(253503932606569/9180151470\) \(9180151470\) \([6]\) \(4608\) \(0.68158\)  
3570.j3 3570j3 \([1, 0, 1, -284, -26854]\) \(-2520453225529/309519000000\) \(-309519000000\) \([2]\) \(6912\) \(0.88432\)  
3570.j4 3570j1 \([1, 0, 1, 31, 992]\) \(3449795831/425079900\) \(-425079900\) \([6]\) \(2304\) \(0.33501\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3570.j have rank \(1\).

Complex multiplication

The elliptic curves in class 3570.j do not have complex multiplication.

Modular form 3570.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - 6 q^{11} + q^{12} + 2 q^{13} - q^{14} - q^{15} + q^{16} - q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.