Elliptic curve isogeny class with Cremona label 180336t (LMFDB label 180336.cv)

• Label: 180336t
• Number of curves: $2$
• Conductor: $180336$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 180336t have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(13\)	\(1 + T\)
\(17\)	\(1\)

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
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 180336t do not have complex multiplication.

Modular form 180336.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 180336t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
180336.cv1	180336t1	\([0, 1, 0, -8179952, 3223214292]\)	\(612241204436497/308834353152\)	\(30533675043949639630848\)	\([2]\)	\(12386304\)	\(3.0070\)	\(\Gamma_0(N)\)-optimal
180336.cv2	180336t2	\([0, 1, 0, 30291728, 24905853140]\)	\(31091549545392623/20700995942016\)	\(-2046655356596761391529984\)	\([2]\)	\(24772608\)	\(3.3536\)