Properties

Label 67626.w
Number of curves $3$
Conductor $67626$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 67626.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67626.w1 67626bh3 \([1, -1, 1, -1195214, 503239389]\) \(-10730978619193/6656\) \(-117120891603456\) \([]\) \(907200\) \(2.0203\)  
67626.w2 67626bh2 \([1, -1, 1, -11759, 981087]\) \(-10218313/17576\) \(-309272354390376\) \([]\) \(302400\) \(1.4710\)  
67626.w3 67626bh1 \([1, -1, 1, 1246, -28101]\) \(12167/26\) \(-457503482826\) \([]\) \(100800\) \(0.92169\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 67626.w have rank \(0\).

Complex multiplication

The elliptic curves in class 67626.w do not have complex multiplication.

Modular form 67626.2.a.w

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.