Properties

Label 92400.fy
Number of curves $2$
Conductor $92400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("fy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.fy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.fy1 92400gi2 \([0, 1, 0, -36229908, 83913539688]\) \(1314817350433665559504/190690249278375\) \(762760997113500000000\) \([2]\) \(7741440\) \(3.0219\)  
92400.fy2 92400gi1 \([0, 1, 0, -2058033, 1559320938]\) \(-3856034557002072064/1973796785296875\) \(-493449196324218750000\) \([2]\) \(3870720\) \(2.6753\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 92400.fy have rank \(0\).

Complex multiplication

The elliptic curves in class 92400.fy do not have complex multiplication.

Modular form 92400.2.a.fy

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.