Elliptic curve isogeny class with Cremona label 75712cx (LMFDB label 75712.cn)

• Label: 75712cx
• Number of curves: $2$
• Conductor: $75712$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 75712cx have rank \(1\).

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 \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 75712.2.a.cx

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 75712cx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
75712.cn2	75712cx1	\([0, -1, 0, -225, 71681]\)	\(-4/7\)	\(-2214308282368\)	\([2]\)	\(150528\)	\(1.0478\)	\(\Gamma_0(N)\)-optimal
75712.cn1	75712cx2	\([0, -1, 0, -27265, 1721121]\)	\(3543122/49\)	\(31000315953152\)	\([2]\)	\(301056\)	\(1.3944\)