Properties

Label 468270.eb
Number of curves $2$
Conductor $468270$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("eb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 468270.eb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
468270.eb1 468270eb2 [1, -1, 1, -180530087, -933578487201] [2] 103219200 \(\Gamma_0(N)\)-optimal*
468270.eb2 468270eb1 [1, -1, 1, -11168807, -14895159969] [2] 51609600 \(\Gamma_0(N)\)-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 468270.eb1.

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 468270.2.a.eb

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

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.