Elliptic curve isogeny class with Cremona label 225400be (LMFDB label 225400.cf)

• Label: 225400be
• Number of curves: $2$
• Conductor: $225400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 225400be have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 225400be do not have complex multiplication.

Modular form 225400.2.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 225400be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
225400.cf1	225400be1	\([0, -1, 0, -54308, 3908612]\)	\(109744/23\)	\(3712531844000000\)	\([2]\)	\(1376256\)	\(1.7024\)	\(\Gamma_0(N)\)-optimal
225400.cf2	225400be2	\([0, -1, 0, 117192, 23459612]\)	\(275684/529\)	\(-341552929648000000\)	\([2]\)	\(2752512\)	\(2.0489\)