Properties

Label 46800.d
Number of curves $4$
Conductor $46800$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46800.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.d1 46800do3 \([0, 0, 0, -747075, -238562750]\) \(988345570681/44994560\) \(2099266191360000000\) \([2]\) \(995328\) \(2.2776\)  
46800.d2 46800do1 \([0, 0, 0, -117075, 15327250]\) \(3803721481/26000\) \(1213056000000000\) \([2]\) \(331776\) \(1.7283\) \(\Gamma_0(N)\)-optimal
46800.d3 46800do2 \([0, 0, 0, -45075, 33975250]\) \(-217081801/10562500\) \(-492804000000000000\) \([2]\) \(663552\) \(2.0749\)  
46800.d4 46800do4 \([0, 0, 0, 404925, -907874750]\) \(157376536199/7722894400\) \(-360319361126400000000\) \([2]\) \(1990656\) \(2.6242\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46800.d have rank \(1\).

Complex multiplication

The elliptic curves in class 46800.d do not have complex multiplication.

Modular form 46800.2.a.d

sage: E.q_eigenform(10)
 
\(q - 4q^{7} - 6q^{11} - q^{13} - 6q^{17} - 2q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.