Elliptic curve isogeny class with Cremona label 176400ll (LMFDB label 176400.ca)

• Label: 176400ll
• Number of curves: $2$
• Conductor: $176400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 176400ll have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 176400ll do not have complex multiplication.

Modular form 176400.2.a.ll

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 176400ll

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
176400.ca2	176400ll1	\([0, 0, 0, -36750, 1071875]\)	\(2048\)	\(2680191281250000\)	\([2]\)	\(691200\)	\(1.6538\)	\(\Gamma_0(N)\)-optimal
176400.ca1	176400ll2	\([0, 0, 0, -312375, -66456250]\)	\(78608\)	\(42883060500000000\)	\([2]\)	\(1382400\)	\(2.0003\)