Elliptic curve isogeny class with Cremona label 63162u (LMFDB label 63162.y)

• Label: 63162u
• Number of curves: $4$
• Conductor: $63162$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 63162u have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(11\)	\(1\)
\(29\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + 5 T + 7 T^{2}\)	1.7.f
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 63162u do not have complex multiplication.

Modular form 63162.2.a.u

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.

Elliptic curves in class 63162u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
63162.y4	63162u1	\([1, -1, 0, 41904, 4914432]\)	\(6300872423/11759616\)	\(-15187167391739904\)	\([2]\)	\(368640\)	\(1.7896\)	\(\Gamma_0(N)\)-optimal
63162.y3	63162u2	\([1, -1, 0, -306576, 51959232]\)	\(2467489596697/527529024\)	\(681286837213832256\)	\([2, 2]\)	\(737280\)	\(2.1362\)
63162.y2	63162u3	\([1, -1, 0, -1569816, -711290376]\)	\(331273336732057/22285827432\)	\(28781432291089525608\)	\([2]\)	\(1474560\)	\(2.4828\)
63162.y1	63162u4	\([1, -1, 0, -4619016, 3821894280]\)	\(8438952173768857/560166552\)	\(723437159213172888\)	\([2]\)	\(1474560\)	\(2.4828\)