Elliptic curve isogeny class with Cremona label 383040nk (LMFDB label 383040.nk)

• Label: 383040nk
• Number of curves: $4$
• Conductor: $383040$
• CM: no
• Rank: $1$

Elliptic curves in class 383040nk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
383040.nk3	383040nk1	\([0, 0, 0, -7590252, -8047691696]\)	\(253060782505556761/41184460800\)	\(7870473023835340800\)	\([2]\)	\(9437184\)	\(2.6348\)	\(\Gamma_0(N)\)-optimal
383040.nk2	383040nk2	\([0, 0, 0, -8327532, -6389991344]\)	\(334199035754662681/101099003040000\)	\(19320320351577047040000\)	\([2, 2]\)	\(18874368\)	\(2.9814\)
383040.nk1	383040nk3	\([0, 0, 0, -51228012, 136194043984]\)	\(77799851782095807001/3092322318750000\)	\(590951997864345600000000\)	\([2]\)	\(37748736\)	\(3.3280\)
383040.nk4	383040nk4	\([0, 0, 0, 22776468, -42881204144]\)	\(6837784281928633319/8113766016106800\)	\(-1550564832245673413836800\)	\([2]\)	\(37748736\)	\(3.3280\)

Rank

The elliptic curves in class 383040nk have rank \(1\).

Complex multiplication

The elliptic curves in class 383040nk do not have complex multiplication.

Modular form 383040.2.a.nk

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.