Properties

Label 426888.a
Number of curves $2$
Conductor $426888$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 426888.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
426888.a1 426888a2 \([0, 0, 0, -72588747, -7181264090]\) \(102129622/59049\) \(24456394672174163769219072\) \([2]\) \(145981440\) \(3.5611\)  
426888.a2 426888a1 \([0, 0, 0, -49109907, 132024778270]\) \(63253004/243\) \(50321799736983876068352\) \([2]\) \(72990720\) \(3.2145\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 426888.a1.

Rank

sage: E.rank()
 

The elliptic curves in class 426888.a have rank \(0\).

Complex multiplication

The elliptic curves in class 426888.a do not have complex multiplication.

Modular form 426888.2.a.a

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} - 6 q^{13} + 6 q^{17} + 6 q^{19} + O(q^{20})\) 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.