Elliptic curve isogeny class with Cremona label 53130t (LMFDB label 53130.s)

• Label: 53130t
• Number of curves: $4$
• Conductor: $53130$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 53130t have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1 + T\)
\(11\)	\(1 + T\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 53130t do not have complex multiplication.

Modular form 53130.2.a.t

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 53130t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
53130.s4	53130t1	\([1, 0, 1, -8880329, -2603762548]\)	\(77448107425788419878921609/41892392875786371072000\)	\(41892392875786371072000\)	\([2]\)	\(5898240\)	\(3.0318\)	\(\Gamma_0(N)\)-optimal
53130.s2	53130t2	\([1, 0, 1, -83842249, 293435851916]\)	\(65179715853307296723232286089/520784732418538896000000\)	\(520784732418538896000000\)	\([2, 2]\)	\(11796480\)	\(3.3784\)
53130.s3	53130t3	\([1, 0, 1, -28182249, 677066835916]\)	\(-2475429904568270179255646089/196606057528071366356412000\)	\(-196606057528071366356412000\)	\([2]\)	\(23592960\)	\(3.7249\)
53130.s1	53130t4	\([1, 0, 1, -1338892969, 18856640041292]\)	\(265436898662503851515370589836169/17149152760523437500000\)	\(17149152760523437500000\)	\([2]\)	\(23592960\)	\(3.7249\)