Elliptic curve isogeny class with LMFDB label 740.b (Cremona label 740b)

• Label: 740.b
• Number of curves: $2$
• Conductor: $740$
• CM: no
• Rank: $1$

Elliptic curves in class 740.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
740.b1	740b2	$[0, 1, 0, -12021, -511321]$	$750484394082304/578125$	$148000000$	$[]$	$432$	$0.87559$
740.b2	740b1	$[0, 1, 0, -181, -425]$	$2575826944/1266325$	$324179200$	$[3]$	$144$	$0.32628$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 740.b have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$5$	$1 + T$
$37$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 - T + 3 T^{2}$	1.3.ab
$7$	$1 + T + 7 T^{2}$	1.7.b
$11$	$1 + 3 T + 11 T^{2}$	1.11.d
$13$	$1 + 4 T + 13 T^{2}$	1.13.e
$17$	$1 + 17 T^{2}$	1.17.a
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 740.b do not have complex multiplication.

Modular form 740.2.a.b

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.