Elliptic curve isogeny class with LMFDB label 110670.j (Cremona label 110670k)

• Label: 110670.j
• Number of curves: $2$
• Conductor: $110670$
• CM: no
• Rank: $1$

Elliptic curves in class 110670.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
110670.j1	110670k2	$[1, 1, 0, -7217, -37779]$	$41580322225044121/23540365585800$	$23540365585800$	$[2]$	$442368$	$1.2558$
110670.j2	110670k1	$[1, 1, 0, 1783, -3579]$	$626321182331879/370523160000$	$-370523160000$	$[2]$	$221184$	$0.90920$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 110670.j have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$3$	$1 + T$
$5$	$1 - T$
$7$	$1 + T$
$17$	$1 + T$
$31$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 - 6 T + 11 T^{2}$	1.11.ag
$13$	$1 + 4 T + 13 T^{2}$	1.13.e
$19$	$1 - 6 T + 19 T^{2}$	1.19.ag
$23$	$1 - 4 T + 23 T^{2}$	1.23.ae
$29$	$1 - 4 T + 29 T^{2}$	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 110670.j do not have complex multiplication.

Modular form 110670.2.a.j

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.