Elliptic curve isogeny class with Cremona label 630e (LMFDB label 630.d)

• Label: 630e
• Number of curves: $4$
• Conductor: $630$
• CM: no
• Rank: $1$

Elliptic curves in class 630e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
630.d4	630e1	$[1, -1, 0, 21, 53]$	$1367631/2800$	$-2041200$	$[2]$	$128$	$-0.10485$	$\Gamma_0(N)$-optimal
630.d3	630e2	$[1, -1, 0, -159, 665]$	$611960049/122500$	$89302500$	$[2, 2]$	$256$	$0.24172$
630.d2	630e3	$[1, -1, 0, -789, -7777]$	$74565301329/5468750$	$3986718750$	$[2]$	$512$	$0.58829$
630.d1	630e4	$[1, -1, 0, -2409, 46115]$	$2121328796049/120050$	$87516450$	$[2]$	$512$	$0.58829$

Rank

The elliptic curves in class 630e have rank $1$.

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 630e do not have complex multiplication.

Modular form 630.2.a.e

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.

$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.