Properties

Label 229320.l
Number of curves $2$
Conductor $229320$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 229320.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.l1 229320ck2 \([0, 0, 0, -484725003, -4105969337498]\) \(1936101054887046531846/905403781953125\) \(5890121600329905120000000\) \([2]\) \(63995904\) \(3.7089\)  
229320.l2 229320ck1 \([0, 0, 0, -25350003, -85794962498]\) \(-553867390580563692/657061767578125\) \(-2137263940743750000000000\) \([2]\) \(31997952\) \(3.3624\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 229320.2.a.l

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.