Elliptic curve isogeny class with Cremona label 76050ct (LMFDB label 76050.cu)

• Label: 76050ct
• Number of curves: $2$
• Conductor: $76050$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 76050ct have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(13\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 76050ct do not have complex multiplication.

Modular form 76050.2.a.ct

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 76050ct

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
76050.cu2	76050ct1	\([1, -1, 0, 455508, 2549221416]\)	\(7604375/2047032\)	\(-2813664483815371875000\)	\([]\)	\(4354560\)	\(2.7949\)	\(\Gamma_0(N)\)-optimal
76050.cu1	76050ct2	\([1, -1, 0, -127878867, 556722719541]\)	\(-168256703745625/30371328\)	\(-41745672231751800000000\)	\([]\)	\(13063680\)	\(3.3442\)