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Properties

Label 468270ee
Number of curves $2$
Conductor $468270$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("ee1")
 
E.isogeny_class()
 

Elliptic curves in class 468270ee

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
468270.ee1 468270ee1 \([1, -1, 1, -208022, 33722021]\) \(770842973809/66873600\) \(86365112371718400\) \([2]\) \(7168000\) \(1.9905\) \(\Gamma_0(N)\)-optimal
468270.ee2 468270ee2 \([1, -1, 1, 227578, 156038501]\) \(1009328859791/8734528080\) \(-11280363239651069520\) \([2]\) \(14336000\) \(2.3371\)  

Rank

sage: E.rank()
 

The elliptic curves in class 468270ee have rank \(0\).

Complex multiplication

The elliptic curves in class 468270ee do not have complex multiplication.

Modular form 468270.2.a.ee

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + 4 q^{7} + q^{8} + q^{10} + 6 q^{13} + 4 q^{14} + q^{16} - 4 q^{17} + 2 q^{19} + O(q^{20})\) Copy content 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 Cremona 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 Cremona labels.