Elliptic curve isogeny class with LMFDB label 64350.ci (Cremona label 64350bn)

• Label: 64350.ci
• Number of curves: $4$
• Conductor: $64350$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 64350.ci have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 - T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 64350.ci do not have complex multiplication.

Modular form 64350.2.a.ci

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 64350.ci

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
64350.ci1	64350bn4	\([1, -1, 0, -14664492, 21616094416]\)	\(30618029936661765625/3678951124992\)	\(41905552658112000000\)	\([2]\)	\(3981312\)	\(2.7898\)
64350.ci2	64350bn3	\([1, -1, 0, -840492, 396254416]\)	\(-5764706497797625/2612665516032\)	\(-29759893143552000000\)	\([2]\)	\(1990656\)	\(2.4433\)
64350.ci3	64350bn2	\([1, -1, 0, -405117, -56444459]\)	\(645532578015625/252306960048\)	\(2873933966796750000\)	\([2]\)	\(1327104\)	\(2.2405\)
64350.ci4	64350bn1	\([1, -1, 0, 80883, -6386459]\)	\(5137417856375/4510142208\)	\(-51373338588000000\)	\([2]\)	\(663552\)	\(1.8940\)	\(\Gamma_0(N)\)-optimal