Properties

Label 450800.l
Number of curves $2$
Conductor $450800$
CM no
Rank $1$
Graph

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

Elliptic curves in class 450800.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450800.l1 450800l2 \([0, 1, 0, -11868208, 14729205588]\) \(24553362849625/1755162752\) \(13215561127043072000000\) \([2]\) \(37158912\) \(2.9916\) \(\Gamma_0(N)\)-optimal*
450800.l2 450800l1 \([0, 1, 0, 675792, 1006069588]\) \(4533086375/60669952\) \(-456816587702272000000\) \([2]\) \(18579456\) \(2.6450\) \(\Gamma_0(N)\)-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 450800.l1.

Rank

sage: E.rank()
 

The elliptic curves in class 450800.l have rank \(1\).

Complex multiplication

The elliptic curves in class 450800.l do not have complex multiplication.

Modular form 450800.2.a.l

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + q^{9} - 4q^{11} + 6q^{17} - 6q^{19} + O(q^{20})\)  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.