Properties

Label 233450.u
Number of curves $4$
Conductor $233450$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 233450.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
233450.u1 233450u3 \([1, -1, 0, -288855467, 1889668389941]\) \(170586815436843383543017473/2166416\) \(33850250000\) \([2]\) \(19660800\) \(3.0069\)  
233450.u2 233450u4 \([1, -1, 0, -18099467, 29371441941]\) \(41966336340198080824833/442001722607124848\) \(6906276915736325750000\) \([2]\) \(19660800\) \(3.0069\)  
233450.u3 233450u2 \([1, -1, 0, -18053467, 29529451941]\) \(41647175116728660507393/4693358285056\) \(73333723204000000\) \([2, 2]\) \(9830400\) \(2.6604\)  
233450.u4 233450u1 \([1, -1, 0, -1125467, 464075941]\) \(-10090256344188054273/107965577101312\) \(-1686962142208000000\) \([2]\) \(4915200\) \(2.3138\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 233450.u have rank \(1\).

Complex multiplication

The elliptic curves in class 233450.u do not have complex multiplication.

Modular form 233450.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} - 3q^{9} + 4q^{11} - 6q^{13} - q^{14} + q^{16} - 6q^{17} + 3q^{18} + 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.