Elliptic curve isogeny class with Cremona label 13754d (LMFDB label 13754.e)

• Label: 13754d
• Number of curves: $3$
• Conductor: $13754$
• CM: no
• Rank: $1$

Elliptic curves in class 13754d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13754.e3	13754d1	$[1, 0, 1, 253, -2528]$	$12167/26$	$-3848933114$	$[]$	$8448$	$0.52352$	$\Gamma_0(N)$-optimal
13754.e2	13754d2	$[1, 0, 1, -2392, 89518]$	$-10218313/17576$	$-2601878785064$	$[]$	$25344$	$1.0728$
13754.e1	13754d3	$[1, 0, 1, -243087, 46110402]$	$-10730978619193/6656$	$-985326877184$	$[]$	$76032$	$1.6221$

Rank

The elliptic curves in class 13754d have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$13$	$1 + T$
$23$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 3 T^{2}$	1.3.a
$5$	$1 - 2 T + 5 T^{2}$	1.5.ac
$7$	$1 - 4 T + 7 T^{2}$	1.7.ae
$11$	$1 + 5 T + 11 T^{2}$	1.11.f
$17$	$1 + 7 T + 17 T^{2}$	1.17.h
$19$	$1 + 7 T + 19 T^{2}$	1.19.h
$29$	$1 - 5 T + 29 T^{2}$	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 13754d do not have complex multiplication.

Modular form 13754.2.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 Cremona numbering.

$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.