Properties

Label 30926k
Number of curves $2$
Conductor $30926$
CM no
Rank $0$
Graph

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

Elliptic curves in class 30926k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30926.m2 30926k1 \([1, 0, 0, 1, 17]\) \(47/56\) \(-123704\) \([]\) \(4992\) \(-0.34387\) \(\Gamma_0(N)\)-optimal
30926.m1 30926k2 \([1, 0, 0, -469, 3871]\) \(-5165405233/686\) \(-1515374\) \([]\) \(14976\) \(0.20544\)  

Rank

sage: E.rank()
 

The elliptic curves in class 30926k have rank \(0\).

Complex multiplication

The elliptic curves in class 30926k do not have complex multiplication.

Modular form 30926.2.a.k

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.