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Properties

Label 570.m
Number of curves $4$
Conductor $570$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 570.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
570.m1 570m4 \([1, 0, 0, -3040, 64262]\) \(3107086841064961/570\) \(570\) \([2]\) \(384\) \(0.36452\)  
570.m2 570m3 \([1, 0, 0, -220, 650]\) \(1177918188481/488703750\) \(488703750\) \([2]\) \(384\) \(0.36452\)  
570.m3 570m2 \([1, 0, 0, -190, 992]\) \(758800078561/324900\) \(324900\) \([2, 2]\) \(192\) \(0.017942\)  
570.m4 570m1 \([1, 0, 0, -10, 20]\) \(-111284641/123120\) \(-123120\) \([4]\) \(96\) \(-0.32863\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 570.m have rank \(0\).

Complex multiplication

The elliptic curves in class 570.m do not have complex multiplication.

Modular form 570.2.a.m

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.