Properties

Label 33600.fj
Number of curves $2$
Conductor $33600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fj1")
 
E.isogeny_class()
 

Elliptic curves in class 33600.fj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.fj1 33600hn2 \([0, 1, 0, -230993, 42640143]\) \(665567485783184/257298363\) \(526947047424000\) \([2]\) \(258048\) \(1.7902\)  
33600.fj2 33600hn1 \([0, 1, 0, -12293, 868443]\) \(-1605176213504/1640558367\) \(-209991470976000\) \([2]\) \(129024\) \(1.4436\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 33600.fj have rank \(1\).

Complex multiplication

The elliptic curves in class 33600.fj do not have complex multiplication.

Modular form 33600.2.a.fj

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} - 4 q^{11} - 6 q^{13} - 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.