Elliptic curve isogeny class with Cremona label 453882bf (LMFDB label 453882.bf)

• Label: 453882bf
• Number of curves: $4$
• Conductor: $453882$
• CM: no
• Rank: $1$

Elliptic curves in class 453882bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
453882.bf4	453882bf1	\([1, 0, 1, 190164, -22934678]\)	\(5137417856375/4510142208\)	\(-667662911277702912\)	\([2]\)	\(7299072\)	\(2.1077\)	\(\Gamma_0(N)\)-optimal^*
453882.bf3	453882bf2	\([1, 0, 1, -952476, -203928854]\)	\(645532578015625/252306960048\)	\(37350485131593162672\)	\([2]\)	\(14598144\)	\(2.4543\)	\(\Gamma_0(N)\)-optimal^*
453882.bf2	453882bf3	\([1, 0, 1, -1976091, 1427589670]\)	\(-5764706497797625/2612665516032\)	\(-386768262325440872448\)	\([2]\)	\(21897216\)	\(2.6570\)	\(\Gamma_0(N)\)-optimal^*
453882.bf1	453882bf4	\([1, 0, 1, -34477851, 77910731302]\)	\(30618029936661765625/3678951124992\)	\(544616800375740837888\)	\([2]\)	\(43794432\)	\(3.0036\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 453882bf1.

Rank

The elliptic curves in class 453882bf have rank \(1\).

Complex multiplication

The elliptic curves in class 453882bf do not have complex multiplication.

Modular form 453882.2.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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.