Elliptic curve isogeny class with LMFDB label 318402.bk (Cremona label 318402bk)

• Label: 318402.bk
• Number of curves: $4$
• Conductor: $318402$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 318402.bk have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 318402.bk do not have complex multiplication.

Modular form 318402.2.a.bk

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 318402.bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
318402.bk1	318402bk4	\([1, -1, 0, -1747579227, -28118792007181]\)	\(5417927574172875/247646\)	\(26979410486633660025642\)	\([2]\)	\(119439360\)	\(3.7842\)
318402.bk2	318402bk3	\([1, -1, 0, -109400937, -437838169735]\)	\(1329185824875/8941324\)	\(974098715464773198820548\)	\([2]\)	\(59719680\)	\(3.4376\)
318402.bk3	318402bk2	\([1, -1, 0, -23432397, -31533372963]\)	\(9521387989875/2634569336\)	\(393716161812780740539368\)	\([2]\)	\(39813120\)	\(3.2349\)
318402.bk4	318402bk1	\([1, -1, 0, -8573637, 9271753749]\)	\(466385893875/21509824\)	\(3214478066994565019712\)	\([2]\)	\(19906560\)	\(2.8883\)	\(\Gamma_0(N)\)-optimal