Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.t1 92400ez4 \([0, -1, 0, -106476448, -422843595008]\) \(260744057755293612689909/8504954620259328\) \(4354536765572775936000\) \([2]\) \(9216000\) \(3.2462\)  
92400.t2 92400ez3 \([0, -1, 0, -6943648, -6000228608]\) \(72313087342699809269/11447096545640448\) \(5860913431367909376000\) \([2]\) \(4608000\) \(2.8996\)  
92400.t3 92400ez2 \([0, -1, 0, -1884048, 986880192]\) \(1444540994277943589/15251205665388\) \(7808617300678656000\) \([2]\) \(1843200\) \(2.4414\)  
92400.t4 92400ez1 \([0, -1, 0, -1879248, 992198592]\) \(1433528304665250149/162339408\) \(83117776896000\) \([2]\) \(921600\) \(2.0949\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 92400.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - q^{11} + 4q^{13} - 2q^{17} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.