Properties

Label 58800.fq
Number of curves $6$
Conductor $58800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fq1")
 
E.isogeny_class()
 

Elliptic curves in class 58800.fq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.fq1 58800do6 \([0, 1, 0, -29890408, -62893928812]\) \(784478485879202/221484375\) \(833837287500000000000\) \([2]\) \(4718592\) \(2.9954\)  
58800.fq2 58800do4 \([0, 1, 0, -2107408, -715574812]\) \(549871953124/200930625\) \(378228593610000000000\) \([2, 2]\) \(2359296\) \(2.6488\)  
58800.fq3 58800do2 \([0, 1, 0, -906908, 324058188]\) \(175293437776/4862025\) \(2288049516900000000\) \([2, 2]\) \(1179648\) \(2.3023\)  
58800.fq4 58800do1 \([0, 1, 0, -900783, 328762188]\) \(2748251600896/2205\) \(64854011250000\) \([2]\) \(589824\) \(1.9557\) \(\Gamma_0(N)\)-optimal
58800.fq5 58800do3 \([0, 1, 0, 195592, 1062733188]\) \(439608956/259416045\) \(-488320612451280000000\) \([2]\) \(2359296\) \(2.6488\)  
58800.fq6 58800do5 \([0, 1, 0, 6467592, -5054524812]\) \(7947184069438/7533176175\) \(-28360660602002400000000\) \([2]\) \(4718592\) \(2.9954\)  

Rank

sage: E.rank()
 

The elliptic curves in class 58800.fq have rank \(1\).

Complex multiplication

The elliptic curves in class 58800.fq do not have complex multiplication.

Modular form 58800.2.a.fq

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - 4 q^{11} - 2 q^{13} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.