Properties

Label 426888fs
Number of curves $4$
Conductor $426888$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("fs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 426888fs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
426888.fs3 426888fs1 \([0, 0, 0, -31321430679, 2133587707068202]\) \(87364831012240243408/1760913\) \(68493560753116942426368\) \([2]\) \(530841600\) \(4.3652\) \(\Gamma_0(N)\)-optimal
426888.fs2 426888fs2 \([0, 0, 0, -31322497899, 2133435040606870]\) \(21843440425782779332/3100814593569\) \(482444806185813657755371815936\) \([2, 2]\) \(1061683200\) \(4.7118\)  
426888.fs4 426888fs3 \([0, 0, 0, -28498633779, 2533737546665710]\) \(-8226100326647904626/4152140742401883\) \(-1292033867409442523577874904930304\) \([2]\) \(2123366400\) \(5.0583\)  
426888.fs1 426888fs4 \([0, 0, 0, -34163437539, 1723361881022782]\) \(14171198121996897746/4077720290568771\) \(1268876236162898623238620879362048\) \([2]\) \(2123366400\) \(5.0583\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 426888.2.a.fs

sage: E.q_eigenform(10)
 
\(q + 2q^{5} - 6q^{13} + 2q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.