Elliptic curve isogeny class with Cremona label 14a (LMFDB label 14.a)

• Label: 14a
• Number of curves: $6$
• Conductor: $14$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 14a have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$7$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 2 T + 3 T^{2}$	1.3.c
$5$	$1 + 5 T^{2}$	1.5.a
$11$	$1 + 11 T^{2}$	1.11.a
$13$	$1 + 4 T + 13 T^{2}$	1.13.e
$17$	$1 - 6 T + 17 T^{2}$	1.17.ag
$19$	$1 - 2 T + 19 T^{2}$	1.19.ac
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 6 T + 29 T^{2}$	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 14a do not have complex multiplication.

Modular form 14.2.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.

$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 3 & 6 & 6 \\ 2 & 1 & 6 & 6 & 3 & 3 \\ 3 & 6 & 1 & 9 & 2 & 18 \\ 3 & 6 & 9 & 1 & 18 & 2 \\ 6 & 3 & 2 & 18 & 1 & 9 \\ 6 & 3 & 18 & 2 & 9 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 14a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
14.a6	14a1	$[1, 0, 1, 4, -6]$	$9938375/21952$	$-21952$	$[6]$	$1$	$-0.48278$	$\Gamma_0(N)$-optimal
14.a3	14a2	$[1, 0, 1, -36, -70]$	$4956477625/941192$	$941192$	$[6]$	$2$	$-0.13621$
14.a2	14a3	$[1, 0, 1, -171, -874]$	$-548347731625/1835008$	$-1835008$	$[2]$	$3$	$0.066527$
14.a5	14a4	$[1, 0, 1, -1, 0]$	$-15625/28$	$-28$	$[6]$	$3$	$-1.0321$
14.a1	14a5	$[1, 0, 1, -2731, -55146]$	$2251439055699625/25088$	$25088$	$[2]$	$6$	$0.41310$
14.a4	14a6	$[1, 0, 1, -11, 12]$	$128787625/98$	$98$	$[6]$	$6$	$-0.68551$