Elliptic curve isogeny class with Cremona label 28050bi (LMFDB label 28050.z)

• Label: 28050bi
• Number of curves: $4$
• Conductor: $28050$
• CM: no
• Rank: $1$

Elliptic curves in class 28050bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
28050.z3	28050bi1	\([1, 0, 1, -9676, 365498]\)	\(6411014266033/296208\)	\(4628250000\)	\([2]\)	\(49152\)	\(0.92983\)	\(\Gamma_0(N)\)-optimal
28050.z2	28050bi2	\([1, 0, 1, -10176, 325498]\)	\(7457162887153/1370924676\)	\(21420698062500\)	\([2, 2]\)	\(98304\)	\(1.2764\)
28050.z4	28050bi3	\([1, 0, 1, 20074, 1898498]\)	\(57258048889007/132611470002\)	\(-2072054218781250\)	\([2]\)	\(196608\)	\(1.6230\)
28050.z1	28050bi4	\([1, 0, 1, -48426, -3805502]\)	\(803760366578833/65593817586\)	\(1024903399781250\)	\([2]\)	\(196608\)	\(1.6230\)

Rank

The elliptic curves in class 28050bi have rank \(1\).

Complex multiplication

The elliptic curves in class 28050bi do not have complex multiplication.

Modular form 28050.2.a.bi

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.