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Properties

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

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 3570.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3570.l1 3570m3 \([1, 0, 1, -3737723, -2781668122]\) \(5774905528848578698851241/31070538632700000\) \(31070538632700000\) \([2]\) \(115200\) \(2.3591\)  
3570.l2 3570m4 \([1, 0, 1, -751803, 200572006]\) \(46993202771097749198761/9805297851562500000\) \(9805297851562500000\) \([2]\) \(115200\) \(2.3591\)  
3570.l3 3570m2 \([1, 0, 1, -237723, -41868122]\) \(1485712211163154851241/103233690000000000\) \(103233690000000000\) \([2, 2]\) \(57600\) \(2.0125\)  
3570.l4 3570m1 \([1, 0, 1, 13157, -2831194]\) \(251907898698209879/3611226931200000\) \(-3611226931200000\) \([2]\) \(28800\) \(1.6659\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3570.2.a.l

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