Elliptic curve isogeny class with Cremona label 83205c (LMFDB label 83205.h)

• Label: 83205c
• Number of curves: $2$
• Conductor: $83205$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 83205c have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 83205c do not have complex multiplication.

Modular form 83205.2.a.c

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 83205c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
83205.h2	83205c1	\([1, -1, 1, -127928, 769906]\)	\(1860867/1075\)	\(133755143060477025\)	\([2]\)	\(709632\)	\(1.9757\)	\(\Gamma_0(N)\)-optimal
83205.h1	83205c2	\([1, -1, 1, -1376003, -618774524]\)	\(2315685267/9245\)	\(1150294230320102415\)	\([2]\)	\(1419264\)	\(2.3223\)