Elliptic curve isogeny class with Cremona label 299538z (LMFDB label 299538.z)

• Label: 299538z
• Number of curves: $2$
• Conductor: $299538$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 299538z have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(43\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 299538z do not have complex multiplication.

Modular form 299538.2.a.z

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 299538z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
299538.z1	299538z1	\([1, -1, 1, -11441, -511451]\)	\(-35937/4\)	\(-18433094650884\)	\([]\)	\(943488\)	\(1.2828\)	\(\Gamma_0(N)\)-optimal
299538.z2	299538z2	\([1, -1, 1, 71764, 719983]\)	\(109503/64\)	\(-23889290667545664\)	\([]\)	\(2830464\)	\(1.8321\)