Elliptic curve isogeny class with LMFDB label 1740.e (Cremona label 1740e)

• Label: 1740.e
• Number of curves: $2$
• Conductor: $1740$
• CM: no
• Rank: $1$

Elliptic curves in class 1740.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1740.e1	1740e2	$[0, 1, 0, -486, -20115]$	$-795070868224/10289109375$	$-164625750000$	$[]$	$1296$	$0.83393$
1740.e2	1740e1	$[0, 1, 0, 54, 729]$	$1068359936/14270175$	$-228322800$	$[3]$	$432$	$0.28463$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 1740.e have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 - T$
$5$	$1 + T$
$29$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + T + 7 T^{2}$	1.7.b
$11$	$1 + 3 T + 11 T^{2}$	1.11.d
$13$	$1 + T + 13 T^{2}$	1.13.b
$17$	$1 - 3 T + 17 T^{2}$	1.17.ad
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 + 23 T^{2}$	1.23.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1740.e do not have complex multiplication.

Modular form 1740.2.a.e

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.