Elliptic curve isogeny class with LMFDB label 75712.bu (Cremona label 75712bt)

• Label: 75712.bu
• Number of curves: $4$
• Conductor: $75712$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 75712.bu have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 75712.bu do not have complex multiplication.

Modular form 75712.2.a.bu

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 75712.bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
75712.bu1	75712bt4	\([0, 0, 0, -639589964, -6223771098480]\)	\(22868021811807457713/8953460393696\)	\(11328983717494232465801216\)	\([2]\)	\(23224320\)	\(3.7722\)
75712.bu2	75712bt3	\([0, 0, 0, -338472524, 2350626226832]\)	\(3389174547561866673/74853681183008\)	\(94713786405296186712915968\)	\([2]\)	\(23224320\)	\(3.7722\)
75712.bu3	75712bt2	\([0, 0, 0, -46007884, -65950600560]\)	\(8511781274893233/3440817243136\)	\(4353731496908956113043456\)	\([2, 2]\)	\(11612160\)	\(3.4256\)
75712.bu4	75712bt1	\([0, 0, 0, 9370036, -7493668208]\)	\(71903073502287/60782804992\)	\(-76909639153911209132032\)	\([2]\)	\(5806080\)	\(3.0791\)	\(\Gamma_0(N)\)-optimal