Properties

Label 229320.z
Number of curves $2$
Conductor $229320$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 229320.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.z1 229320du1 \([0, 0, 0, -8668443, -4624536602]\) \(820221748268836/369468094905\) \(32448353621259994629120\) \([2]\) \(14450688\) \(3.0148\) \(\Gamma_0(N)\)-optimal
229320.z2 229320du2 \([0, 0, 0, 30086637, -34628719538]\) \(17147425715207422/12872524043925\) \(-2261046179280242411366400\) \([2]\) \(28901376\) \(3.3613\)  

Rank

sage: E.rank()
 

The elliptic curves in class 229320.z have rank \(1\).

Complex multiplication

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

Modular form 229320.2.a.z

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.