Properties

Label 3570.i
Number of curves $2$
Conductor $3570$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 3570.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3570.i1 3570h2 \([1, 1, 0, -21597, -1230669]\) \(1114128841413009241/57352050\) \(57352050\) \([2]\) \(6144\) \(0.96142\)  
3570.i2 3570h1 \([1, 1, 0, -1347, -19719]\) \(-270601485933241/1951897500\) \(-1951897500\) \([2]\) \(3072\) \(0.61485\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3570.i have rank \(0\).

Complex multiplication

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

Modular form 3570.2.a.i

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.