Properties

Label 304920.e
Number of curves $2$
Conductor $304920$
CM no
Rank $0$
Graph

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

Elliptic curves in class 304920.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
304920.e1 304920e1 \([0, 0, 0, -109758, -13985543]\) \(9419041273856/8103375\) \(125803146546000\) \([2]\) \(1990656\) \(1.6320\) \(\Gamma_0(N)\)-optimal
304920.e2 304920e2 \([0, 0, 0, -85503, -20335502]\) \(-278305777136/558140625\) \(-138640202316000000\) \([2]\) \(3981312\) \(1.9786\)  

Rank

sage: E.rank()
 

The elliptic curves in class 304920.e have rank \(0\).

Complex multiplication

The elliptic curves in class 304920.e do not have complex multiplication.

Modular form 304920.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 6 q^{13} + 8 q^{17} - 2 q^{19} + O(q^{20})\) 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.