Properties

Label 92400.s
Number of curves $2$
Conductor $92400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.s1 92400d1 \([0, -1, 0, -157008, -23893488]\) \(26752959989284/169785\) \(2716560000000\) \([2]\) \(479232\) \(1.5709\) \(\Gamma_0(N)\)-optimal
92400.s2 92400d2 \([0, -1, 0, -154008, -24853488]\) \(-12624273557282/1067664675\) \(-34165269600000000\) \([2]\) \(958464\) \(1.9175\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92400.s have rank \(1\).

Complex multiplication

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

Modular form 92400.2.a.s

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