Elliptic curve isogeny class with Cremona label 1045b (LMFDB label 1045.b)

• Label: 1045b
• Number of curves: $4$
• Conductor: $1045$
• CM: no
• Rank: $1$

Elliptic curves in class 1045b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1045.b3	1045b1	\([1, -1, 0, -982409, -374543312]\)	\(104857852278310619039721/47155625\)	\(47155625\)	\([2]\)	\(4416\)	\(1.7158\)	\(\Gamma_0(N)\)-optimal
1045.b2	1045b2	\([1, -1, 0, -982414, -374539305]\)	\(104859453317683374662841/2223652969140625\)	\(2223652969140625\)	\([2, 2]\)	\(8832\)	\(2.0624\)
1045.b1	1045b3	\([1, -1, 0, -1016789, -346894930]\)	\(116256292809537371612841/15216540068579856875\)	\(15216540068579856875\)	\([4]\)	\(17664\)	\(2.4090\)
1045.b4	1045b4	\([1, -1, 0, -948119, -401927292]\)	\(-94256762600623910012361/15323275604248046875\)	\(-15323275604248046875\)	\([2]\)	\(17664\)	\(2.4090\)

Rank

The elliptic curves in class 1045b have rank \(1\).

Complex multiplication

The elliptic curves in class 1045b do not have complex multiplication.

Modular form 1045.2.a.b

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.