Elliptic curve isogeny class with LMFDB label 2445.c (Cremona label 2445c)

• Label: 2445.c
• Number of curves: $4$
• Conductor: $2445$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 2445.c have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(163\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2445.c do not have complex multiplication.

Modular form 2445.2.a.c

Isogeny matrix

The \((i,j)\)-th entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 2445.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2445.c1	2445c3	\([1, 0, 1, -7034, 222041]\)	\(38480618749557529/857682789615\)	\(857682789615\)	\([2]\)	\(3840\)	\(1.0772\)
2445.c2	2445c2	\([1, 0, 1, -959, -6379]\)	\(97393143178729/39221822025\)	\(39221822025\)	\([2, 2]\)	\(1920\)	\(0.73067\)
2445.c3	2445c1	\([1, 0, 1, -834, -9329]\)	\(64043209720729/24755625\)	\(24755625\)	\([2]\)	\(960\)	\(0.38410\)	\(\Gamma_0(N)\)-optimal
2445.c4	2445c4	\([1, 0, 1, 3116, -45499]\)	\(3347467708032071/2841729286815\)	\(-2841729286815\)	\([2]\)	\(3840\)	\(1.0772\)