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Properties

Label 34914.k
Number of curves $2$
Conductor $34914$
CM no
Rank $2$
Graph

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

Elliptic curves in class 34914.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34914.k1 34914s2 \([1, 0, 1, -15789868, 17736568682]\) \(2940980566145956489/783792101714688\) \(116029360568512262437632\) \([2]\) \(8110080\) \(3.1341\)  
34914.k2 34914s1 \([1, 0, 1, 2492372, 1794455402]\) \(11566328890520951/16088147361792\) \(-2381623197065883353088\) \([2]\) \(4055040\) \(2.7875\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 34914.k have rank \(2\).

Complex multiplication

The elliptic curves in class 34914.k do not have complex multiplication.

Modular form 34914.2.a.k

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.