↑

Properties

Label 249690.v
Number of curves $2$
Conductor $249690$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 249690.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
249690.v1 249690v2 \([1, 0, 1, -10809898, -13725606244]\) \(-139697438374379634892156441/531351792476467200000\) \(-531351792476467200000\) \([]\) \(21384000\) \(2.8359\)  
249690.v2 249690v1 \([1, 0, 1, 299477, -98649994]\) \(2970408770986067593559/5925260742187500000\) \(-5925260742187500000\) \([3]\) \(7128000\) \(2.2866\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 249690.v have rank \(0\).

Complex multiplication

The elliptic curves in class 249690.v do not have complex multiplication.

Modular form 249690.2.a.v

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.