Properties

Label 466752ef
Number of curves $2$
Conductor $466752$
CM no
Rank $1$
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Show commands: SageMath
sage: E = EllipticCurve("ef1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 466752ef

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
466752.ef1 466752ef1 \([0, 1, 0, -2525281, -1323593953]\) \(6793805286030262681/1048227429629952\) \(274786531312914137088\) \([2]\) \(28901376\) \(2.6453\) \(\Gamma_0(N)\)-optimal
466752.ef2 466752ef2 \([0, 1, 0, 4396959, -7297487073]\) \(35862531227445945959/108547797844556928\) \(-28455153918163531333632\) \([2]\) \(57802752\) \(2.9919\)  

Rank

sage: E.rank()
 

The elliptic curves in class 466752ef have rank \(1\).

Complex multiplication

The elliptic curves in class 466752ef do not have complex multiplication.

Modular form 466752.2.a.ef

sage: E.q_eigenform(10)
 
\(q + q^{3} + 4 q^{5} + 2 q^{7} + q^{9} + q^{11} + q^{13} + 4 q^{15} - q^{17} - 4 q^{19} + O(q^{20})\)  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 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.