Elliptic curve isogeny class with LMFDB label 2028.f (Cremona label 2028e)

• Label: 2028.f
• Number of curves: $2$
• Conductor: $2028$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 2028.f have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 - T$
$13$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 - 2 T + 5 T^{2}$	1.5.ac
$7$	$1 + 4 T + 7 T^{2}$	1.7.e
$11$	$1 - 6 T + 11 T^{2}$	1.11.ag
$17$	$1 - 2 T + 17 T^{2}$	1.17.ac
$19$	$1 + 19 T^{2}$	1.19.a
$23$	$1 - 8 T + 23 T^{2}$	1.23.ai
$29$	$1 - 2 T + 29 T^{2}$	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2028.f do not have complex multiplication.

Modular form 2028.2.a.f

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.

$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 2028.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2028.f1	2028e2	$[0, 1, 0, -212, -1260]$	$1882384/3$	$1687296$	$[2]$	$576$	$0.092613$
2028.f2	2028e1	$[0, 1, 0, -17, -12]$	$16384/9$	$316368$	$[2]$	$288$	$-0.25396$	$\Gamma_0(N)$-optimal