Properties

Label 47190.b
Number of curves $2$
Conductor $47190$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47190.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.b1 47190f2 \([1, 1, 0, -1952061663, 33195389531517]\) \(464352938845529653759213009/2445173327025000\) \(4331773704397736025000\) \([2]\) \(19353600\) \(3.7684\)  
47190.b2 47190f1 \([1, 1, 0, -121936663, 519239706517]\) \(-113180217375258301213009/260161419375000000\) \(-460891824269394375000000\) \([2]\) \(9676800\) \(3.4219\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 47190.b have rank \(1\).

Complex multiplication

The elliptic curves in class 47190.b do not have complex multiplication.

Modular form 47190.2.a.b

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