Elliptic curve isogeny class with Cremona label 226576be (LMFDB label 226576.bt)

• Label: 226576be
• Number of curves: $2$
• Conductor: $226576$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 226576be have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 226576be do not have complex multiplication.

Modular form 226576.2.a.be

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 226576be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
226576.bt1	226576be1	\([0, 0, 0, -172126955, 821100463386]\)	\(9869198625/614656\)	\(35125345587687664127049728\)	\([2]\)	\(40108032\)	\(3.6532\)	\(\Gamma_0(N)\)-optimal
226576.bt2	226576be2	\([0, 0, 0, 136016405, 3439271335962]\)	\(4869777375/92236816\)	\(-5270997172252380098065399808\)	\([2]\)	\(80216064\)	\(3.9997\)