Elliptic curve isogeny class with LMFDB label 2475.j (Cremona label 2475a)

• Label: 2475.j
• Number of curves: $2$
• Conductor: $2475$
• CM: no
• Rank: $1$

Elliptic curves in class 2475.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2475.j1	2475a2	$[1, -1, 0, -417, 3366]$	$19034163/121$	$51046875$	$[2]$	$640$	$0.31603$
2475.j2	2475a1	$[1, -1, 0, -42, -9]$	$19683/11$	$4640625$	$[2]$	$320$	$-0.030545$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 2475.j have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$3$	$1$
$5$	$1$
$11$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 - T + 2 T^{2}$	1.2.ab
$7$	$1 - 2 T + 7 T^{2}$	1.7.ac
$13$	$1 - 2 T + 13 T^{2}$	1.13.ac
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 + 6 T + 19 T^{2}$	1.19.g
$23$	$1 + 4 T + 23 T^{2}$	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 2475.j do not have complex multiplication.

Modular form 2475.2.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.