Elliptic curve isogeny class with Cremona label 760a (LMFDB label 760.d)

• Label: 760a
• Number of curves: $2$
• Conductor: $760$
• CM: no
• Rank: $0$

Elliptic curves in class 760a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
760.d2	760a1	$[0, -1, 0, 5, 0]$	$702464/475$	$-7600$	$[2]$	$64$	$-0.56666$	$\Gamma_0(N)$-optimal
760.d1	760a2	$[0, -1, 0, -20, 20]$	$3631696/1805$	$462080$	$[2]$	$128$	$-0.22008$

Rank

The elliptic curves in class 760a have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$5$	$1 - T$
$19$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 2 T + 3 T^{2}$	1.3.c
$7$	$1 + 7 T^{2}$	1.7.a
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 - 4 T + 13 T^{2}$	1.13.ae
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$23$	$1 + 4 T + 23 T^{2}$	1.23.e
$29$	$1 + 6 T + 29 T^{2}$	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 760a do not have complex multiplication.

Modular form 760.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.