Properties

Label 450840t
Number of curves $2$
Conductor $450840$
CM no
Rank $2$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 450840t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450840.t1 450840t1 \([0, -1, 0, -980, 5700]\) \(82843472/38025\) \(47825107200\) \([2]\) \(344064\) \(0.74406\) \(\Gamma_0(N)\)-optimal
450840.t2 450840t2 \([0, -1, 0, 3440, 39292]\) \(894594172/658125\) \(-3310968960000\) \([2]\) \(688128\) \(1.0906\)  

Rank

sage: E.rank()
 

The elliptic curves in class 450840t have rank \(2\).

Complex multiplication

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

Modular form 450840.2.a.t

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