Elliptic curve isogeny class with LMFDB label 158025.n (Cremona label 158025g)

• Label: 158025.n
• Number of curves: $4$
• Conductor: $158025$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 158025.n have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(43\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 158025.n do not have complex multiplication.

Modular form 158025.2.a.n

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 158025.n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
158025.n1	158025g4	\([1, 0, 0, -299538, -62349183]\)	\(1616855892553/22851963\)	\(42007978046671875\)	\([2]\)	\(1474560\)	\(1.9945\)
158025.n2	158025g2	\([1, 0, 0, -36163, 1124192]\)	\(2845178713/1347921\)	\(2477836839515625\)	\([2, 2]\)	\(737280\)	\(1.6479\)
158025.n3	158025g1	\([1, 0, 0, -30038, 2000067]\)	\(1630532233/1161\)	\(2134226390625\)	\([2]\)	\(368640\)	\(1.3014\)	\(\Gamma_0(N)\)-optimal
158025.n4	158025g3	\([1, 0, 0, 129212, 8566067]\)	\(129784785047/92307627\)	\(-169685937639421875\)	\([2]\)	\(1474560\)	\(1.9945\)