Elliptic curve isogeny class with Cremona label 124950be (LMFDB label 124950.g)

• Label: 124950be
• Number of curves: $4$
• Conductor: $124950$
• CM: no
• Rank: $1$

Elliptic curves in class 124950be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
124950.g3	124950be1	\([1, 1, 0, -1243400, 521352000]\)	\(115650783909361/2924544000\)	\(5376088704000000000\)	\([2]\)	\(3538944\)	\(2.3768\)	\(\Gamma_0(N)\)-optimal
124950.g2	124950be2	\([1, 1, 0, -2811400, -1060760000]\)	\(1336852858103281/509796000000\)	\(937140462562500000000\)	\([2, 2]\)	\(7077888\)	\(2.7234\)
124950.g4	124950be3	\([1, 1, 0, 8850600, -7579818000]\)	\(41709358422320399/37652343750000\)	\(-69215009216308593750000\)	\([2]\)	\(14155776\)	\(3.0700\)
124950.g1	124950be4	\([1, 1, 0, -39561400, -95765510000]\)	\(3725035528036823281/1203203526000\)	\(2211807681724593750000\)	\([2]\)	\(14155776\)	\(3.0700\)

Rank

The elliptic curves in class 124950be have rank \(1\).

Complex multiplication

The elliptic curves in class 124950be do not have complex multiplication.

Modular form 124950.2.a.be

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.