Properties

Label 298816.u
Number of curves $4$
Conductor $298816$
CM no
Rank $2$
Graph

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

Elliptic curves in class 298816.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
298816.u1 298816u3 \([0, 0, 0, -739469996, 7739785937200]\) \(170586815436843383543017473/2166416\) \(567912955904\) \([2]\) \(29491200\) \(3.2419\)  
298816.u2 298816u4 \([0, 0, 0, -46334636, 120286892336]\) \(41966336340198080824833/442001722607124848\) \(115868099571122136154112\) \([2]\) \(29491200\) \(3.2419\)  
298816.u3 298816u2 \([0, 0, 0, -46216876, 120934148400]\) \(41647175116728660507393/4693358285056\) \(1230335714277720064\) \([2, 2]\) \(14745600\) \(2.8954\)  
298816.u4 298816u1 \([0, 0, 0, -2881196, 1899702576]\) \(-10090256344188054273/107965577101312\) \(-28302528243646332928\) \([2]\) \(7372800\) \(2.5488\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 298816.u have rank \(2\).

Complex multiplication

The elliptic curves in class 298816.u do not have complex multiplication.

Modular form 298816.2.a.u

sage: E.q_eigenform(10)
 
\(q - 2q^{5} - q^{7} - 3q^{9} - 4q^{11} - 6q^{13} + 6q^{17} - 4q^{19} + O(q^{20})\)  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.