Elliptic curve isogeny class with LMFDB label 77760.bs (Cremona label 77760dx)

• Label: 77760.bs
• Number of curves: $2$
• Conductor: $77760$
• CM: no
• Rank: $1$

Elliptic curves in class 77760.bs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
77760.bs1	77760dx2	$[0, 0, 0, -47628, 3961872]$	$28588707/320$	$133741506723840$	$[]$	$248832$	$1.5245$
77760.bs2	77760dx1	$[0, 0, 0, -4428, -110448]$	$16747803/500$	$286654464000$	$[]$	$82944$	$0.97523$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 77760.bs have rank $1$.

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 - T + 7 T^{2}$	1.7.ab
$11$	$1 - 3 T + 11 T^{2}$	1.11.ad
$13$	$1 - 4 T + 13 T^{2}$	1.13.ae
$17$	$1 + 3 T + 17 T^{2}$	1.17.d
$19$	$1 - 2 T + 19 T^{2}$	1.19.ac
$23$	$1 - 6 T + 23 T^{2}$	1.23.ag
$29$	$1 + 6 T + 29 T^{2}$	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 77760.bs do not have complex multiplication.

Modular form 77760.2.a.bs

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.