Elliptic curve isogeny class with LMFDB label 10304.i (Cremona label 10304j)

• Label: 10304.i
• Number of curves: $2$
• Conductor: $10304$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 10304.i have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1 - T\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 10304.i do not have complex multiplication.

Modular form 10304.2.a.i

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 10304.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10304.i1	10304j2	\([0, 1, 0, -38753, 2736127]\)	\(24553362849625/1755162752\)	\(460105384460288\)	\([2]\)	\(43008\)	\(1.5605\)
10304.i2	10304j1	\([0, 1, 0, 2207, 188415]\)	\(4533086375/60669952\)	\(-15904263897088\)	\([2]\)	\(21504\)	\(1.2139\)	\(\Gamma_0(N)\)-optimal