Elliptic curve isogeny class with Cremona label 61152bf (LMFDB label 61152.f)

• Label: 61152bf
• Number of curves: $2$
• Conductor: $61152$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 61152bf have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 61152bf do not have complex multiplication.

Modular form 61152.2.a.bf

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.

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

Isogeny graph

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

Elliptic curves in class 61152bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
61152.f2	61152bf1	\([0, -1, 0, -250994, -48443772]\)	\(-232245467895232/709540923\)	\(-5342513923201728\)	\([2]\)	\(368640\)	\(1.8865\)	\(\Gamma_0(N)\)-optimal
61152.f1	61152bf2	\([0, -1, 0, -4018849, -3099652751]\)	\(14896378491692608/138411\)	\(66698918866944\)	\([2]\)	\(737280\)	\(2.2331\)