Properties

Label 405600.g
Number of curves $4$
Conductor $405600$
CM no
Rank $0$
Graph

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

Elliptic curves in class 405600.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405600.g1 405600g2 \([0, -1, 0, -961273408, 11468232029812]\) \(2543984126301795848/909361981125\) \(35114532758015841000000000\) \([2]\) \(198180864\) \(3.8710\) \(\Gamma_0(N)\)-optimal*
405600.g2 405600g4 \([0, -1, 0, -496523408, -4170763907688]\) \(350584567631475848/8259273550125\) \(318927487241642409000000000\) \([2]\) \(198180864\) \(3.8710\)  
405600.g3 405600g1 \([0, -1, 0, -68742158, 124159842312]\) \(7442744143086784/2927948765625\) \(14132649453457640625000000\) \([2, 2]\) \(99090432\) \(3.5244\) \(\Gamma_0(N)\)-optimal*
405600.g4 405600g3 \([0, -1, 0, 220437967, 895981595937]\) \(3834800837445824/3342041015625\) \(-1032409193765625000000000000\) \([2]\) \(198180864\) \(3.8710\)  
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 405600.g1.

Rank

sage: E.rank()
 

The elliptic curves in class 405600.g have rank \(0\).

Complex multiplication

The elliptic curves in class 405600.g do not have complex multiplication.

Modular form 405600.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4q^{7} + q^{9} - 2q^{17} + 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.