Elliptic curve isogeny class with Cremona label 349690cu (LMFDB label 349690.cu)

• Label: 349690cu
• Number of curves: $4$
• Conductor: $349690$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 349690cu have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 - T\)
\(11\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 349690cu do not have complex multiplication.

Modular form 349690.2.a.cu

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 349690cu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
349690.cu2	349690cu1	\([1, 1, 1, -89294070, -324807002893]\)	\(1841373668746009/31443200\)	\(1344548205279371628800\)	\([2]\)	\(49766400\)	\(3.1837\)	\(\Gamma_0(N)\)-optimal
349690.cu3	349690cu2	\([1, 1, 1, -86496550, -346106201165]\)	\(-1673672305534489/241375690000\)	\(-10321508332089926269210000\)	\([2]\)	\(99532800\)	\(3.5303\)
349690.cu1	349690cu3	\([1, 1, 1, -145769005, 133184507875]\)	\(8010684753304969/4456448000000\)	\(190562956706723397632000000\)	\([2]\)	\(149299200\)	\(3.7330\)
349690.cu4	349690cu4	\([1, 1, 1, 570396115, 1055318716387]\)	\(479958568556831351/289000000000000\)	\(-12357979827935401000000000000\)	\([2]\)	\(298598400\)	\(4.0796\)