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Properties

Label 3570v
Number of curves $8$
Conductor $3570$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 3570v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3570.w7 3570v1 \([1, 0, 0, -32326, 2663780]\) \(-3735772816268612449/909650165760000\) \(-909650165760000\) \([6]\) \(18432\) \(1.5888\) \(\Gamma_0(N)\)-optimal
3570.w6 3570v2 \([1, 0, 0, -544326, 154522980]\) \(17836145204788591940449/770635366502400\) \(770635366502400\) \([2, 6]\) \(36864\) \(1.9353\)  
3570.w8 3570v3 \([1, 0, 0, 232634, -18120604]\) \(1392333139184610040991/947901937500000000\) \(-947901937500000000\) \([2]\) \(55296\) \(2.1381\)  
3570.w5 3570v4 \([1, 0, 0, -571526, 138219300]\) \(20645800966247918737249/3688936444974392640\) \(3688936444974392640\) \([6]\) \(73728\) \(2.2819\)  
3570.w3 3570v5 \([1, 0, 0, -8709126, 9891863460]\) \(73054578035931991395831649/136386452160\) \(136386452160\) \([6]\) \(73728\) \(2.2819\)  
3570.w4 3570v6 \([1, 0, 0, -1017366, -151370604]\) \(116454264690812369959009/57505157319440250000\) \(57505157319440250000\) \([2, 2]\) \(110592\) \(2.4846\)  
3570.w1 3570v7 \([1, 0, 0, -13299866, -18656185104]\) \(260174968233082037895439009/223081361502731896500\) \(223081361502731896500\) \([2]\) \(221184\) \(2.8312\)  
3570.w2 3570v8 \([1, 0, 0, -8734866, 9830443896]\) \(73704237235978088924479009/899277423164136103500\) \(899277423164136103500\) \([2]\) \(221184\) \(2.8312\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3570.2.a.v

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

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.