Properties

Label 92400b
Number of curves $4$
Conductor $92400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.o4 92400b1 \([0, -1, 0, 9092, -322688]\) \(20777545136/23059575\) \(-92238300000000\) \([2]\) \(196608\) \(1.3661\) \(\Gamma_0(N)\)-optimal
92400.o3 92400b2 \([0, -1, 0, -51408, -2984688]\) \(939083699236/300155625\) \(4802490000000000\) \([2, 2]\) \(393216\) \(1.7127\)  
92400.o2 92400b3 \([0, -1, 0, -326408, 69615312]\) \(120186986927618/4332064275\) \(138626056800000000\) \([2]\) \(786432\) \(2.0593\)  
92400.o1 92400b4 \([0, -1, 0, -744408, -246920688]\) \(1425631925916578/270703125\) \(8662500000000000\) \([2]\) \(786432\) \(2.0593\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 92400.2.a.b

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.