Properties

Label 150075s
Number of curves $2$
Conductor $150075$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 150075s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
150075.v2 150075s1 \([0, 0, 1, -27904800, -50555649344]\) \(210966209738334797824/25153051046653125\) \(286508972078283251953125\) \([]\) \(12441600\) \(3.2320\) \(\Gamma_0(N)\)-optimal
150075.v1 150075s2 \([0, 0, 1, -535288800, 4759595300281]\) \(1489157481162281146384384/2616603057861328125\) \(29804744205951690673828125\) \([]\) \(37324800\) \(3.7813\)  

Rank

sage: E.rank()
 

The elliptic curves in class 150075s have rank \(0\).

Complex multiplication

The elliptic curves in class 150075s do not have complex multiplication.

Modular form 150075.2.a.s

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