Properties

Label 450840u
Number of curves $2$
Conductor $450840$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 450840u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450840.u1 450840u1 \([0, -1, 0, -449567340, -3668785137900]\) \(330999787611942608/200201625\) \(6077820308479669152000\) \([2]\) \(97763328\) \(3.5022\) \(\Gamma_0(N)\)-optimal
450840.u2 450840u2 \([0, -1, 0, -446914320, -3714227125668]\) \(-81293584906713092/2036310046875\) \(-247277244772774687536000000\) \([2]\) \(195526656\) \(3.8488\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 450840.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 2q^{7} + q^{9} + 4q^{11} - q^{13} - q^{15} + 8q^{19} + O(q^{20})\)  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.