Elliptic curve isogeny class with Cremona label 28314p (LMFDB label 28314.r)

• Label: 28314p
• Number of curves: $4$
• Conductor: $28314$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 28314p have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(17\)	\( 1 - 8 T + 17 T^{2}\)	1.17.ai
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 28314p do not have complex multiplication.

Modular form 28314.2.a.p

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 28314p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
28314.r4	28314p1	\([1, -1, 0, 391473, 67689837]\)	\(5137417856375/4510142208\)	\(-5824704197266935552\)	\([2]\)	\(552960\)	\(2.2882\)	\(\Gamma_0(N)\)-optimal
28314.r3	28314p2	\([1, -1, 0, -1960767, 602589213]\)	\(645532578015625/252306960048\)	\(325846357257754702512\)	\([2]\)	\(1105920\)	\(2.6348\)
28314.r2	28314p3	\([1, -1, 0, -4067982, -4216062636]\)	\(-5764706497797625/2612665516032\)	\(-3374173827666183979008\)	\([2]\)	\(1658880\)	\(2.8375\)
28314.r1	28314p4	\([1, -1, 0, -70976142, -230111392428]\)	\(30618029936661765625/3678951124992\)	\(4751247537443683381248\)	\([2]\)	\(3317760\)	\(3.1841\)