Elliptic curve isogeny class with Cremona label 401115bk (LMFDB label 401115.bk)

• Label: 401115bk
• Number of curves: $4$
• Conductor: $401115$
• CM: no
• Rank: $1$

Elliptic curves in class 401115bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
401115.bk3	401115bk1	\([1, 1, 0, -3148, -66557]\)	\(1948441249/89505\)	\(158563567305\)	\([2]\)	\(573440\)	\(0.91076\)	\(\Gamma_0(N)\)-optimal^*
401115.bk2	401115bk2	\([1, 1, 0, -8593, 217672]\)	\(39616946929/10989225\)	\(19468082430225\)	\([2, 2]\)	\(1146880\)	\(1.2573\)	\(\Gamma_0(N)\)-optimal^*
401115.bk1	401115bk3	\([1, 1, 0, -126568, 17276857]\)	\(126574061279329/16286595\)	\(28852696524795\)	\([2]\)	\(2293760\)	\(1.6039\)	\(\Gamma_0(N)\)-optimal^*
401115.bk4	401115bk4	\([1, 1, 0, 22262, 1458043]\)	\(688699320191/910381875\)	\(-1612797024856875\)	\([2]\)	\(2293760\)	\(1.6039\)

^*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 401115bk1.

Rank

The elliptic curves in class 401115bk have rank \(1\).

Complex multiplication

The elliptic curves in class 401115bk do not have complex multiplication.

Modular form 401115.2.a.bk

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.