Elliptic curve isogeny class with Cremona label 6090h (LMFDB label 6090.g)

• Label: 6090h
• Number of curves: $2$
• Conductor: $6090$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 6090h have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$3$	$1 - T$
$5$	$1 + T$
$7$	$1 + T$
$29$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 - 4 T + 11 T^{2}$	1.11.ae
$13$	$1 - 6 T + 13 T^{2}$	1.13.ag
$17$	$1 - 6 T + 17 T^{2}$	1.17.ag
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 + 23 T^{2}$	1.23.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6090h do not have complex multiplication.

Modular form 6090.2.a.h

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.

Elliptic curves in class 6090h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6090.g1	6090h1	$[1, 0, 1, -3699, 86266]$	$5595100866606889/6394500$	$6394500$	$[2]$	$4224$	$0.59039$	$\Gamma_0(N)$-optimal
6090.g2	6090h2	$[1, 0, 1, -3669, 87742]$	$-5460050774992969/189303843750$	$-189303843750$	$[2]$	$8448$	$0.93696$