Properties

Label 3570.c
Number of curves $2$
Conductor $3570$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3570.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3570.c1 3570c2 \([1, 1, 0, -518, 3132]\) \(15417797707369/4080067320\) \(4080067320\) \([2]\) \(2304\) \(0.55269\)  
3570.c2 3570c1 \([1, 1, 0, 82, 372]\) \(59822347031/83966400\) \(-83966400\) \([2]\) \(1152\) \(0.20612\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3570.2.a.c

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