Elliptic curve isogeny class with LMFDB label 10304.t (Cremona label 10304bj)

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

Rank

The elliptic curves in class 10304.t 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 \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 10304.2.a.t

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.t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10304.t1	10304bj2	\([0, 0, 0, -3916, -94320]\)	\(50668941906/1127\)	\(147718144\)	\([2]\)	\(4096\)	\(0.68251\)
10304.t2	10304bj1	\([0, 0, 0, -236, -1584]\)	\(-22180932/3703\)	\(-242679808\)	\([2]\)	\(2048\)	\(0.33594\)	\(\Gamma_0(N)\)-optimal