Elliptic curve isogeny class with Cremona label 90944eb (LMFDB label 90944.by)

• Label: 90944eb
• Number of curves: $2$
• Conductor: $90944$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 90944eb have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(29\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 90944eb do not have complex multiplication.

Modular form 90944.2.a.eb

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 90944eb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
90944.by1	90944eb1	\([0, -1, 0, -849, 15121]\)	\(-35152/29\)	\(-55899275264\)	\([]\)	\(73728\)	\(0.76021\)	\(\Gamma_0(N)\)-optimal
90944.by2	90944eb2	\([0, -1, 0, 6991, -243599]\)	\(19600688/24389\)	\(-47011290497024\)	\([]\)	\(221184\)	\(1.3095\)