Properties

Label 59290.cf
Number of curves $2$
Conductor $59290$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cf1")
 
E.isogeny_class()
 

Elliptic curves in class 59290.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59290.cf1 59290f1 \([1, -1, 0, -780775, -265350079]\) \(-5154200289/20\) \(-204253932487220\) \([]\) \(1176000\) \(1.9591\) \(\Gamma_0(N)\)-optimal
59290.cf2 59290f2 \([1, -1, 0, 5444675, 2518173125]\) \(1747829720511/1280000000\) \(-13072251679182080000000\) \([]\) \(8232000\) \(2.9320\)  

Rank

sage: E.rank()
 

The elliptic curves in class 59290.cf have rank \(0\).

Complex multiplication

The elliptic curves in class 59290.cf do not have complex multiplication.

Modular form 59290.2.a.cf

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.