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

• Label: 150a
• Number of curves: $4$
• Conductor: $150$
• CM: no
• Rank: $0$

Elliptic curves in class 150a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
150.c4	150a1	$[1, 0, 0, -3, -3]$	$-24389/12$	$-1500$	$[2]$	$8$	$-0.68527$	$\Gamma_0(N)$-optimal
150.c2	150a2	$[1, 0, 0, -53, -153]$	$131872229/18$	$2250$	$[2]$	$16$	$-0.33870$
150.c3	150a3	$[1, 0, 0, -28, 272]$	$-19465109/248832$	$-31104000$	$[10]$	$40$	$0.11945$
150.c1	150a4	$[1, 0, 0, -828, 9072]$	$502270291349/1889568$	$236196000$	$[10]$	$80$	$0.46602$

Rank

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

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$3$	$1 + T$
$5$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 - 2 T + 7 T^{2}$	1.7.ac
$11$	$1 - 2 T + 11 T^{2}$	1.11.ac
$13$	$1 - 6 T + 13 T^{2}$	1.13.ag
$17$	$1 - 2 T + 17 T^{2}$	1.17.ac
$19$	$1 + 19 T^{2}$	1.19.a
$23$	$1 + 4 T + 23 T^{2}$	1.23.e
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 150.2.a.a

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.

$\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.