↑

Properties

Label 95550.b
Number of curves $2$
Conductor $95550$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 95550.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.b1 95550cx2 \([1, 1, 0, -3210, -64350]\) \(248858189/27378\) \(402624290250\) \([2]\) \(196608\) \(0.96020\)  
95550.b2 95550cx1 \([1, 1, 0, -760, 6700]\) \(3307949/468\) \(6882466500\) \([2]\) \(98304\) \(0.61363\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 95550.b have rank \(2\).

Complex multiplication

The elliptic curves in class 95550.b do not have complex multiplication.

Modular form 95550.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.