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Properties

Label 35574.k
Number of curves $2$
Conductor $35574$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 35574.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35574.k1 35574d2 \([1, 1, 0, -836112, 304958592]\) \(-6329617441/279936\) \(-2858901442237120896\) \([]\) \(699720\) \(2.3064\)  
35574.k2 35574d1 \([1, 1, 0, -6052, -420482]\) \(-2401/6\) \(-61276179746166\) \([]\) \(99960\) \(1.3334\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 35574.k have rank \(0\).

Complex multiplication

The elliptic curves in class 35574.k do not have complex multiplication.

Modular form 35574.2.a.k

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.