Properties

Label 4620a
Number of curves $2$
Conductor $4620$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4620a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4620.a2 4620a1 \([0, -1, 0, -21, 126]\) \(-67108864/343035\) \(-5488560\) \([2]\) \(960\) \(-0.022504\) \(\Gamma_0(N)\)-optimal
4620.a1 4620a2 \([0, -1, 0, -516, 4680]\) \(59466754384/121275\) \(31046400\) \([2]\) \(1920\) \(0.32407\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4620a have rank \(1\).

Complex multiplication

The elliptic curves in class 4620a do not have complex multiplication.

Modular form 4620.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} + q^{11} - 6q^{13} + q^{15} + 2q^{17} + O(q^{20})\)  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.