Elliptic curve isogeny class with Cremona label 295845f (LMFDB label 295845.f)

• Label: 295845f
• Number of curves: $4$
• Conductor: $295845$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 295845f have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(11\)	\(1\)
\(163\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 295845f do not have complex multiplication.

Modular form 295845.2.a.f

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 Cremona 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 Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 295845f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
295845.f3	295845f1	\([1, 0, 0, -100856, 12315711]\)	\(64043209720729/24755625\)	\(43856099780625\)	\([2]\)	\(1228800\)	\(1.5830\)	\(\Gamma_0(N)\)-optimal
295845.f2	295845f2	\([1, 0, 0, -115981, 8374136]\)	\(97393143178729/39221822025\)	\(69483850248431025\)	\([2, 2]\)	\(2457600\)	\(1.9296\)
295845.f4	295845f3	\([1, 0, 0, 377094, 60935931]\)	\(3347467708032071/2841729286815\)	\(-5034296777079268215\)	\([2]\)	\(4915200\)	\(2.2762\)
295845.f1	295845f4	\([1, 0, 0, -851056, -296387959]\)	\(38480618749557529/857682789615\)	\(1519437380453139015\)	\([2]\)	\(4915200\)	\(2.2762\)