Properties

Label 46800.l
Number of curves $2$
Conductor $46800$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46800.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.l1 46800dl2 \([0, 0, 0, -484275, -129734030]\) \(-168256703745625/30371328\) \(-2267207486668800\) \([]\) \(373248\) \(1.9502\)  
46800.l2 46800dl1 \([0, 0, 0, 1725, -594110]\) \(7604375/2047032\) \(-152810119987200\) \([]\) \(124416\) \(1.4009\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 46800.2.a.l

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.