Elliptic curve isogeny class with Cremona label 374850la (LMFDB label 374850.la)

• Label: 374850la
• Number of curves: $4$
• Conductor: $374850$
• CM: no
• Rank: $2$

Elliptic curves in class 374850la

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
374850.la4	374850la1	\([1, -1, 1, 10795, 116650797]\)	\(103823/4386816\)	\(-5878752997824000000\)	\([2]\)	\(9437184\)	\(2.2804\)	\(\Gamma_0(N)\)-optimal
374850.la3	374850la2	\([1, -1, 1, -3517205, 2494522797]\)	\(3590714269297/73410624\)	\(98377257197961000000\)	\([2, 2]\)	\(18874368\)	\(2.6270\)
374850.la1	374850la3	\([1, -1, 1, -55996205, 161295976797]\)	\(14489843500598257/6246072\)	\(8370333858229875000\)	\([2]\)	\(37748736\)	\(2.9735\)
374850.la2	374850la4	\([1, -1, 1, -7486205, -4165459203]\)	\(34623662831857/14438442312\)	\(19348893599726746125000\)	\([2]\)	\(37748736\)	\(2.9735\)

Rank

The elliptic curves in class 374850la have rank \(2\).

Complex multiplication

The elliptic curves in class 374850la do not have complex multiplication.

Modular form 374850.2.a.la

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.