Elliptic curve isogeny class with LMFDB label 3234.n (Cremona label 3234n)

• Label: 3234.n
• Number of curves: $4$
• Conductor: $3234$
• CM: no
• Rank: $0$

Elliptic curves in class 3234.n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3234.n1	3234n4	$[1, 0, 1, -11100, 448984]$	$1285429208617/614922$	$72344958378$	$[2]$	$6144$	$1.0386$
3234.n2	3234n3	$[1, 0, 1, -6200, -185272]$	$223980311017/4278582$	$503370893718$	$[2]$	$6144$	$1.0386$
3234.n3	3234n2	$[1, 0, 1, -810, 4456]$	$498677257/213444$	$25111473156$	$[2, 2]$	$3072$	$0.69204$
3234.n4	3234n1	$[1, 0, 1, 170, 536]$	$4657463/3696$	$-434830704$	$[2]$	$1536$	$0.34547$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 3234.n have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$3$	$1 - T$
$7$	$1$
$11$	$1 - T$

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 3234.n do not have complex multiplication.

Modular form 3234.2.a.n

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.

$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.