Properties

Label 15210q
Number of curves $2$
Conductor $15210$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 15210q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15210.f2 15210q1 \([1, -1, 0, -104220, 4980496]\) \(16194277/8000\) \(61845440343336000\) \([2]\) \(134784\) \(1.9151\) \(\Gamma_0(N)\)-optimal
15210.f1 15210q2 \([1, -1, 0, -895140, -322302200]\) \(10260751717/125000\) \(966335005364625000\) \([2]\) \(269568\) \(2.2616\)  

Rank

sage: E.rank()
 

The elliptic curves in class 15210q have rank \(1\).

Complex multiplication

The elliptic curves in class 15210q do not have complex multiplication.

Modular form 15210.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + q^{16} - 6 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.