Elliptic curve isogeny class with Cremona label 22050be (LMFDB label 22050.bj)

• Label: 22050be
• Number of curves: $8$
• Conductor: $22050$
• CM: no
• Rank: $1$

Elliptic curves in class 22050be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
22050.bj8	22050be1	$[1, -1, 0, 16308, 2457216]$	$357911/2160$	$-2894606583750000$	$[2]$	$110592$	$1.6487$	$\Gamma_0(N)$-optimal
22050.bj6	22050be2	$[1, -1, 0, -204192, 32224716]$	$702595369/72900$	$97692972201562500$	$[2, 2]$	$221184$	$1.9953$
22050.bj7	22050be3	$[1, -1, 0, -149067, -72457659]$	$-273359449/1536000$	$-2058386904000000000$	$[2]$	$331776$	$2.1980$
22050.bj5	22050be4	$[1, -1, 0, -755442, -217491534]$	$35578826569/5314410$	$7121817673493906250$	$[2]$	$442368$	$2.3418$
22050.bj4	22050be5	$[1, -1, 0, -3180942, 2184414966]$	$2656166199049/33750$	$45228227871093750$	$[2]$	$442368$	$2.3418$
22050.bj3	22050be6	$[1, -1, 0, -3677067, -2707873659]$	$4102915888729/9000000$	$12060860765625000000$	$[2, 2]$	$663552$	$2.5446$
22050.bj1	22050be7	$[1, -1, 0, -58802067, -173540248659]$	$16778985534208729/81000$	$108547746890625000$	$[2]$	$1327104$	$2.8911$
22050.bj2	22050be8	$[1, -1, 0, -5000067, -584458659]$	$10316097499609/5859375000$	$7852122894287109375000$	$[2]$	$1327104$	$2.8911$

Rank

The elliptic curves in class 22050be have rank $1$.

Complex multiplication

The elliptic curves in class 22050be do not have complex multiplication.

Modular form 22050.2.a.be

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.