Properties

Label 75150f
Number of curves 2
Conductor 75150
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("75150.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75150f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
75150.u2 75150f1 [1, -1, 0, -667992, -209979584] [2] 627200 \(\Gamma_0(N)\)-optimal
75150.u1 75150f2 [1, -1, 0, -10687992, -13446399584] [2] 1254400  

Rank

sage: E.rank()
 

The elliptic curves in class 75150f have rank \(0\).

Modular form 75150.2.a.u

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + 2q^{7} - q^{8} - 2q^{14} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.