Properties

Label 4620.e
Number of curves $2$
Conductor $4620$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 4620.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4620.e1 4620e2 \([0, -1, 0, -98619500, -375994125000]\) \(414354576760345737269208016/1182266314178222109375\) \(302660176429624860000000\) \([2]\) \(873600\) \(3.3770\)  
4620.e2 4620e1 \([0, -1, 0, -3697625, -10620843750]\) \(-349439858058052607328256/2844147488104248046875\) \(-45506359809667968750000\) \([2]\) \(436800\) \(3.0305\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4620.e have rank \(0\).

Complex multiplication

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

Modular form 4620.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} - q^{11} + 4 q^{13} - q^{15} + 2 q^{17} + 2 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.