Elliptic curve isogeny class with Cremona label 150c (LMFDB label 150.b)

• Label: 150c
• Number of curves: $8$
• Conductor: $150$
• CM: no
• Rank: $0$

Elliptic curves in class 150c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
150.b8	150c1	$[1, 1, 1, 37, 281]$	$357911/2160$	$-33750000$	$[4]$	$48$	$0.12643$	$\Gamma_0(N)$-optimal
150.b6	150c2	$[1, 1, 1, -463, 3281]$	$702595369/72900$	$1139062500$	$[2, 2]$	$96$	$0.47301$
150.b7	150c3	$[1, 1, 1, -338, -7969]$	$-273359449/1536000$	$-24000000000$	$[4]$	$144$	$0.67574$
150.b5	150c4	$[1, 1, 1, -1713, -24219]$	$35578826569/5314410$	$83037656250$	$[2]$	$192$	$0.81958$
150.b4	150c5	$[1, 1, 1, -7213, 232781]$	$2656166199049/33750$	$527343750$	$[2]$	$192$	$0.81958$
150.b3	150c6	$[1, 1, 1, -8338, -295969]$	$4102915888729/9000000$	$140625000000$	$[2, 2]$	$288$	$1.0223$
150.b1	150c7	$[1, 1, 1, -133338, -18795969]$	$16778985534208729/81000$	$1265625000$	$[2]$	$576$	$1.3689$
150.b2	150c8	$[1, 1, 1, -11338, -67969]$	$10316097499609/5859375000$	$91552734375000$	$[2]$	$576$	$1.3689$

Rank

The elliptic curves in class 150c have rank $0$.

Complex multiplication

The elliptic curves in class 150c do not have complex multiplication.

Modular form 150.2.a.c

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.