Properties

Label 190575.ba
Number of curves $2$
Conductor $190575$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 190575.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190575.ba1 190575bb2 \([1, -1, 1, -78051920, 265406522582]\) \(244738769070151/28588707\) \(6142797819456039559125\) \([2]\) \(22302720\) \(3.2070\)  
190575.ba2 190575bb1 \([1, -1, 1, -5279495, 3425792582]\) \(75740658391/20253807\) \(4351894665095678171625\) \([2]\) \(11151360\) \(2.8604\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 190575.ba have rank \(1\).

Complex multiplication

The elliptic curves in class 190575.ba do not have complex multiplication.

Modular form 190575.2.a.ba

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