Elliptic curve isogeny class with LMFDB label 675.d (Cremona label 675c)

• Label: 675.d
• Number of curves: $2$
• Conductor: $675$
• CM: $\Q(\sqrt{-3})$
• Rank: $0$

Elliptic curves in class 675.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
675.d1	675c2	$[0, 0, 1, 0, -169]$	$0$	$-12301875$	$[]$	$126$	$0.039321$		$-3$
675.d2	675c1	$[0, 0, 1, 0, 6]$	$0$	$-16875$	$[3]$	$42$	$-0.50998$	$\Gamma_0(N)$-optimal	$-3$

Rank

The elliptic curves in class 675.d have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$3$	$1$
$5$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 + 2 T^{2}$	1.2.a
$7$	$1 + 4 T + 7 T^{2}$	1.7.e
$11$	$1 + 11 T^{2}$	1.11.a
$13$	$1 - 5 T + 13 T^{2}$	1.13.af
$17$	$1 + 17 T^{2}$	1.17.a
$19$	$1 - 8 T + 19 T^{2}$	1.19.ai
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 675.d has complex multiplication by an order in the imaginary quadratic field $\Q(\sqrt{-3})$.

Modular form 675.2.a.d

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.

$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.