Properties

Label 4368.f
Number of curves $2$
Conductor $4368$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 4368.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4368.f1 4368a2 \([0, -1, 0, -166388, -26068080]\) \(1989996724085074000/1843096437\) \(471832687872\) \([2]\) \(15360\) \(1.5369\)  
4368.f2 4368a1 \([0, -1, 0, -10323, -410994]\) \(-7604375980288000/236743082667\) \(-3787889322672\) \([2]\) \(7680\) \(1.1903\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4368.f have rank \(1\).

Complex multiplication

The elliptic curves in class 4368.f do not have complex multiplication.

Modular form 4368.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} + 2 q^{11} - q^{13} - 6 q^{17} + 8 q^{19} + O(q^{20})\) 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.