Properties

Label 466752.l
Number of curves $2$
Conductor $466752$
CM no
Rank $0$
Graph

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

Elliptic curves in class 466752.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
466752.l1 466752l2 \([0, -1, 0, -33489, -2347695]\) \(253526452425808/4091373\) \(67033055232\) \([2]\) \(950272\) \(1.2100\) \(\Gamma_0(N)\)-optimal*
466752.l2 466752l1 \([0, -1, 0, -2029, -38531]\) \(-902576293888/126190779\) \(-129219357696\) \([2]\) \(475136\) \(0.86346\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 466752.l1.

Rank

sage: E.rank()
 

The elliptic curves in class 466752.l have rank \(0\).

Complex multiplication

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

Modular form 466752.2.a.l

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