Elliptic curve isogeny class with LMFDB label 29575.f (Cremona label 29575w)

• Label: 29575.f
• Number of curves: $2$
• Conductor: $29575$
• CM: no
• Rank: $1$

Elliptic curves in class 29575.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
29575.f1	29575w2	$[0, 1, 1, -626708, 191710744]$	$-2887553024/16807$	$-158445661841796875$	$[]$	$468000$	$2.1414$
29575.f2	29575w1	$[0, 1, 1, 7042, -315506]$	$4096/7$	$-65991529296875$	$[]$	$93600$	$1.3367$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 29575.f have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$5$	$1$
$7$	$1 - T$
$13$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 + 2 T + 2 T^{2}$	1.2.c
$3$	$1 - T + 3 T^{2}$	1.3.ab
$11$	$1 - 3 T + 11 T^{2}$	1.11.ad
$17$	$1 - 7 T + 17 T^{2}$	1.17.ah
$19$	$1 + 19 T^{2}$	1.19.a
$23$	$1 - 6 T + 23 T^{2}$	1.23.ag
$29$	$1 + 5 T + 29 T^{2}$	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 29575.f do not have complex multiplication.

Modular form 29575.2.a.f

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.

$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.