Elliptic curve isogeny class with Cremona label 158025m (LMFDB label 158025.f)

• Label: 158025m
• Number of curves: $2$
• Conductor: $158025$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 158025m have rank \(1\).

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
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 158025.2.a.m

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 158025m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
158025.f1	158025m1	\([1, 1, 1, -27588, -1739844]\)	\(1263214441/29025\)	\(53355659765625\)	\([2]\)	\(497664\)	\(1.4203\)	\(\Gamma_0(N)\)-optimal
158025.f2	158025m2	\([1, 1, 1, 3037, -5353594]\)	\(1685159/6739605\)	\(-12389184197578125\)	\([2]\)	\(995328\)	\(1.7669\)