Elliptic curve isogeny class with LMFDB label 24150.e (Cremona label 24150d)

• Label: 24150.e
• Number of curves: $8$
• Conductor: $24150$
• CM: no
• Rank: $0$

Elliptic curves in class 24150.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
24150.e1	24150d8	\([1, 1, 0, -6347475400, -182631622775000]\)	\(1810117493172631097464564372609/125368453502655029296875000\)	\(1958882085978984832763671875000\)	\([2]\)	\(47775744\)	\(4.5604\)
24150.e2	24150d6	\([1, 1, 0, -6237972400, -189634449128000]\)	\(1718043013877225552292911401729/9180538178765625000000\)	\(143445909043212890625000000\)	\([2, 2]\)	\(23887872\)	\(4.2139\)
24150.e3	24150d3	\([1, 1, 0, -6237964400, -189634959840000]\)	\(1718036403880129446396978632449/49057344000000\)	\(766521000000000000\)	\([2]\)	\(11943936\)	\(3.8673\)
24150.e4	24150d7	\([1, 1, 0, -6128597400, -196604589753000]\)	\(-1629247127728109256861881401729/125809119536174660320875000\)	\(-1965767492752729067513671875000\)	\([2]\)	\(47775744\)	\(4.5604\)
24150.e5	24150d5	\([1, 1, 0, -1182924400, 15605518432000]\)	\(11715873038622856702991202049/46415372499833400000000\)	\(725240195309896875000000000\)	\([2]\)	\(15925248\)	\(4.0111\)
24150.e6	24150d2	\([1, 1, 0, -109836400, -17569760000]\)	\(9378698233516887309850369/5418996968417034240000\)	\(84671827631516160000000000\)	\([2, 2]\)	\(7962624\)	\(3.6646\)
24150.e7	24150d1	\([1, 1, 0, -77068400, -259758048000]\)	\(3239908336204082689644289/9880281924658790400\)	\(154379405072793600000000\)	\([2]\)	\(3981312\)	\(3.3180\)	\(\Gamma_0(N)\)-optimal
24150.e8	24150d4	\([1, 1, 0, 438963600, -139952160000]\)	\(598672364899527954087397631/346996861747253448998400\)	\(-5421825964800835140600000000\)	\([2]\)	\(15925248\)	\(4.0111\)

Rank

The elliptic curves in class 24150.e have rank \(0\).

Complex multiplication

The elliptic curves in class 24150.e do not have complex multiplication.

Modular form 24150.2.a.e

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 3 & 6 & 12 & 12 \\ 2 & 1 & 2 & 2 & 6 & 3 & 6 & 6 \\ 4 & 2 & 1 & 4 & 12 & 6 & 3 & 12 \\ 4 & 2 & 4 & 1 & 12 & 6 & 12 & 3 \\ 3 & 6 & 12 & 12 & 1 & 2 & 4 & 4 \\ 6 & 3 & 6 & 6 & 2 & 1 & 2 & 2 \\ 12 & 6 & 3 & 12 & 4 & 2 & 1 & 4 \\ 12 & 6 & 12 & 3 & 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.