Elliptic curve isogeny class with LMFDB label 402930.bf (Cremona label 402930bf)

• Label: 402930.bf
• Number of curves: $4$
• Conductor: $402930$
• CM: no
• Rank: $0$

Elliptic curves in class 402930.bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
402930.bf1	402930bf4	\([1, -1, 0, -11420910, -6628519980]\)	\(127568139540190201/59114336463360\)	\(76344272051118182115840\)	\([2]\)	\(52254720\)	\(3.0854\)
402930.bf2	402930bf2	\([1, -1, 0, -5785335, 5357171925]\)	\(16581570075765001/998001000\)	\(1288886324529969000\)	\([2]\)	\(17418240\)	\(2.5361\)	\(\Gamma_0(N)\)-optimal^*
402930.bf3	402930bf1	\([1, -1, 0, -340335, 94034925]\)	\(-3375675045001/999000000\)	\(-1290176501031000000\)	\([2]\)	\(8709120\)	\(2.1895\)	\(\Gamma_0(N)\)-optimal^*
402930.bf4	402930bf3	\([1, -1, 0, 2518290, -782419500]\)	\(1367594037332999/995878502400\)	\(-1286145186865289625600\)	\([2]\)	\(26127360\)	\(2.7388\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 402930.bf1.

Rank

The elliptic curves in class 402930.bf have rank \(0\).

Complex multiplication

The elliptic curves in class 402930.bf do not have complex multiplication.

Modular form 402930.2.a.bf

Isogeny 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.