Elliptic curve isogeny class with Cremona label 410958bw (LMFDB label 410958.bw)

• Label: 410958bw
• Number of curves: $3$
• Conductor: $410958$
• CM: no
• Rank: $1$

Elliptic curves in class 410958bw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
410958.bw3	410958bw1	\([1, -1, 1, -121001, -16169907]\)	\(11134383337/316\)	\(5560426945116\)	\([]\)	\(2073600\)	\(1.5472\)	\(\Gamma_0(N)\)-optimal^*
410958.bw2	410958bw2	\([1, -1, 1, -212036, 11322663]\)	\(59914169497/31554496\)	\(555241993031503296\)	\([]\)	\(6220800\)	\(2.0965\)	\(\Gamma_0(N)\)-optimal^*
410958.bw1	410958bw3	\([1, -1, 1, -13568171, 19240047483]\)	\(15698803397448457/20709376\)	\(364408140275122176\)	\([]\)	\(18662400\)	\(2.6458\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 410958bw1.

Rank

The elliptic curves in class 410958bw have rank \(1\).

Complex multiplication

The elliptic curves in class 410958bw do not have complex multiplication.

Modular form 410958.2.a.bw

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 Cremona numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.