Properties

Label 229320.r
Number of curves $4$
Conductor $229320$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 229320.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.r1 229320ds4 \([0, 0, 0, -11014563, -14070139202]\) \(841356017734178/1404585\) \(246713972868679680\) \([2]\) \(7864320\) \(2.5994\)  
229320.r2 229320ds3 \([0, 0, 0, -1806483, 645071182]\) \(3711757787138/1124589375\) \(197533016906883840000\) \([2]\) \(7864320\) \(2.5994\)  
229320.r3 229320ds2 \([0, 0, 0, -695163, -215312762]\) \(423026849956/16769025\) \(1472731368654873600\) \([2, 2]\) \(3932160\) \(2.2529\)  
229320.r4 229320ds1 \([0, 0, 0, 19257, -12274598]\) \(35969456/2985255\) \(-65544637835738880\) \([2]\) \(1966080\) \(1.9063\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 229320.r have rank \(0\).

Complex multiplication

The elliptic curves in class 229320.r do not have complex multiplication.

Modular form 229320.2.a.r

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