Properties

Label 369600.ta
Number of curves $4$
Conductor $369600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ta1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.ta

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.ta1 369600ta4 \([0, 1, 0, -439605633, -3547797883137]\) \(9175156963749600923236/50249267578125\) \(51455250000000000000000\) \([2]\) \(70778880\) \(3.5514\)  
369600.ta2 369600ta3 \([0, 1, 0, -88713633, 257610304863]\) \(75404081626158563716/15633273575910375\) \(16008472141732224000000000\) \([2]\) \(70778880\) \(3.5514\)  
369600.ta3 369600ta2 \([0, 1, 0, -27963633, -53368945137]\) \(9446361110552374864/661910688140625\) \(169449136164000000000000\) \([2, 2]\) \(35389440\) \(3.2048\)  
369600.ta4 369600ta1 \([0, 1, 0, 1560867, -3620162637]\) \(26284586405881856/369163298455875\) \(-5906612775294000000000\) \([2]\) \(17694720\) \(2.8582\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 369600.ta have rank \(0\).

Complex multiplication

The elliptic curves in class 369600.ta do not have complex multiplication.

Modular form 369600.2.a.ta

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.