Elliptic curve isogeny class with Cremona label 327990w (LMFDB label 327990.w)

• Label: 327990w
• Number of curves: $4$
• Conductor: $327990$
• CM: no
• Rank: $1$

Elliptic curves in class 327990w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
327990.w2	327990w1	\([1, 1, 1, -3507666786, 79959058357983]\)	\(8023996232564328604273609/2693913066000\)	\(1602402316403412186000\)	\([2]\)	\(179988480\)	\(3.8646\)	\(\Gamma_0(N)\)-optimal
327990.w3	327990w2	\([1, 1, 1, -3507179006, 79982408971919]\)	\(-8020649220830773808798089/4649360115706312500\)	\(-2765547824549373061913812500\)	\([2]\)	\(359976960\)	\(4.2112\)
327990.w1	327990w3	\([1, 1, 1, -3566213001, 77151666786999]\)	\(8432523527010257294720569/556754628456000000000\)	\(331170637080319022376000000000\)	\([2]\)	\(539965440\)	\(4.4139\)
327990.w4	327990w4	\([1, 1, 1, 2997354679, 329001009522743]\)	\(5006683449688877689783751/81509038330078125000000\)	\(-48483476871013364501953125000000\)	\([2]\)	\(1079930880\)	\(4.7605\)

Rank

The elliptic curves in class 327990w have rank \(1\).

Complex multiplication

The elliptic curves in class 327990w do not have complex multiplication.

Modular form 327990.2.a.w

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.