Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("eh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 229320.eh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.eh1 229320em1 \([0, 0, 0, -56742, 5194049]\) \(397526095872/739375\) \(37578267090000\) \([2]\) \(688128\) \(1.4955\) \(\Gamma_0(N)\)-optimal
229320.eh2 229320em2 \([0, 0, 0, -38367, 8615474]\) \(-7680778992/34987225\) \(-28451257579180800\) \([2]\) \(1376256\) \(1.8420\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 229320.2.a.eh

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