Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4620h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4620.h2 4620h1 \([0, 1, 0, -82321, -12507496]\) \(-3856034557002072064/1973796785296875\) \(-31580748564750000\) \([2]\) \(40320\) \(1.8706\) \(\Gamma_0(N)\)-optimal
4620.h1 4620h2 \([0, 1, 0, -1449196, -671887996]\) \(1314817350433665559504/190690249278375\) \(48816703815264000\) \([2]\) \(80640\) \(2.2172\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4620.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - q^{7} + q^{9} - q^{11} - q^{15} - 2 q^{17} - 6 q^{19} + O(q^{20})\)  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.