Properties

Label 92400.g
Number of curves $4$
Conductor $92400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.g1 92400dl4 \([0, -1, 0, -36801808, -85919117888]\) \(86129359107301290313/9166294368\) \(586642839552000000\) \([2]\) \(5898240\) \(2.8372\)  
92400.g2 92400dl2 \([0, -1, 0, -2305808, -1334925888]\) \(21184262604460873/216872764416\) \(13879856922624000000\) \([2, 2]\) \(2949120\) \(2.4906\)  
92400.g3 92400dl3 \([0, -1, 0, -577808, -3291021888]\) \(-333345918055753/72923718045024\) \(-4667117954881536000000\) \([2]\) \(5898240\) \(2.8372\)  
92400.g4 92400dl1 \([0, -1, 0, -257808, 16754112]\) \(29609739866953/15259926528\) \(976635297792000000\) \([2]\) \(1474560\) \(2.1440\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 92400.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.