Elliptic curve isogeny class with Cremona label 53361u (LMFDB label 53361.cd)

• Label: 53361u
• Number of curves: $2$
• Conductor: $53361$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 53361u have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 53361u do not have complex multiplication.

Modular form 53361.2.a.u

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.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 53361u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
53361.cd2	53361u1	\([0, 0, 1, -124509, 18375453]\)	\(-28672/3\)	\(-22335167517477507\)	\([]\)	\(470400\)	\(1.8761\)	\(\Gamma_0(N)\)-optimal
53361.cd1	53361u2	\([0, 0, 1, -48683019, -130846808997]\)	\(-1713910976512/1594323\)	\(-11869823760655763797587\)	\([]\)	\(6115200\)	\(3.1586\)