Properties

Label 450840.l
Number of curves $2$
Conductor $450840$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 450840.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450840.l1 450840l2 \([0, -1, 0, -57896, 5299500]\) \(434163602/7605\) \(375943602677760\) \([2]\) \(1892352\) \(1.5932\) \(\Gamma_0(N)\)-optimal*
450840.l2 450840l1 \([0, -1, 0, -96, 236220]\) \(-4/975\) \(-24098948889600\) \([2]\) \(946176\) \(1.2467\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 450840.l1.

Rank

sage: E.rank()
 

The elliptic curves in class 450840.l have rank \(0\).

Complex multiplication

The elliptic curves in class 450840.l do not have complex multiplication.

Modular form 450840.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + 2q^{7} + q^{9} + q^{13} + q^{15} + 6q^{19} + O(q^{20})\)  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 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.