↑

Properties

Label 247962.i
Number of curves $2$
Conductor $247962$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 247962.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
247962.i1 247962i2 \([1, 1, 0, -9859674, 11532172410]\) \(893863401019289/32468145138\) \(3850328385711815021586\) \([2]\) \(16154624\) \(2.9117\)  
247962.i2 247962i1 \([1, 1, 0, -1556704, -502152308]\) \(3518049774329/1119705444\) \(132783490906090549668\) \([2]\) \(8077312\) \(2.5651\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 247962.i have rank \(1\).

Complex multiplication

The elliptic curves in class 247962.i do not have complex multiplication.

Modular form 247962.2.a.i

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.