↑

Properties

Label 185150.l
Number of curves $2$
Conductor $185150$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 185150.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185150.l1 185150bv2 \([1, 1, 0, -694151430, 7039010345230]\) \(-35716427480168065/98\) \(-101494952473440050\) \([]\) \(35054208\) \(3.3822\)  
185150.l2 185150bv1 \([1, 1, 0, -8540980, 9720645560]\) \(-66531687265/941192\) \(-974757523554918240200\) \([]\) \(11684736\) \(2.8329\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 185150.l have rank \(1\).

Complex multiplication

The elliptic curves in class 185150.l do not have complex multiplication.

Modular form 185150.2.a.l

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