Elliptic curve isogeny class with Cremona label 350350dc (LMFDB label 350350.dc)

• Label: 350350dc
• Number of curves: $2$
• Conductor: $350350$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 350350dc have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 350350dc do not have complex multiplication.

Modular form 350350.2.a.dc

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 350350dc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
350350.dc2	350350dc1	\([1, 1, 0, 24475, 1345625]\)	\(881974079/929500\)	\(-1708667898437500\)	\([2]\)	\(1990656\)	\(1.6096\)	\(\Gamma_0(N)\)-optimal
350350.dc1	350350dc2	\([1, 1, 0, -134775, 12333875]\)	\(147281603041/49156250\)	\(90362244628906250\)	\([2]\)	\(3981312\)	\(1.9562\)