Elliptic curve isogeny class with Cremona label 293046bz (LMFDB label 293046.bz)

• Label: 293046bz
• Number of curves: $2$
• Conductor: $293046$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 293046bz have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(13\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 293046bz do not have complex multiplication.

Modular form 293046.2.a.bz

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 293046bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
293046.bz2	293046bz1	\([1, 1, 1, -284671, 84203621]\)	\(-48109395853/30081024\)	\(-1595203894882271232\)	\([2]\)	\(7962624\)	\(2.1945\)	\(\Gamma_0(N)\)-optimal
293046.bz1	293046bz2	\([1, 1, 1, -5093631, 4421885541]\)	\(275602131611533/53934336\)	\(2860150733402197248\)	\([2]\)	\(15925248\)	\(2.5410\)