Elliptic curve isogeny class with LMFDB label 1682.i (Cremona label 1682f)

• Label: 1682.i
• Number of curves: $2$
• Conductor: $1682$
• CM: no
• Rank: $0$

Elliptic curves in class 1682.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1682.i1	1682f2	$[1, 1, 1, -148, -755]$	$426477625/8$	$6728$	$[]$	$300$	$-0.14116$
1682.i2	1682f1	$[1, 1, 1, -3, -1]$	$3625/2$	$1682$	$[]$	$100$	$-0.69047$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 1682.i have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 - T$
$29$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 - 2 T + 3 T^{2}$	1.3.ac
$5$	$1 + 5 T^{2}$	1.5.a
$7$	$1 + T + 7 T^{2}$	1.7.b
$11$	$1 - 6 T + 11 T^{2}$	1.11.ag
$13$	$1 + 4 T + 13 T^{2}$	1.13.e
$17$	$1 - 3 T + 17 T^{2}$	1.17.ad
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 - 9 T + 23 T^{2}$	1.23.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1682.i do not have complex multiplication.

Modular form 1682.2.a.i

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.