Elliptic curve isogeny class with Cremona label 330096l (LMFDB label 330096.l)

• Label: 330096l
• Number of curves: $2$
• Conductor: $330096$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 330096l have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(13\)	\(1 + T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 330096l do not have complex multiplication.

Modular form 330096.2.a.l

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 330096l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
330096.l2	330096l1	\([0, -1, 0, 31, -696]\)	\(16384/1053\)	\(-204989616\)	\([2]\)	\(92160\)	\(0.27448\)	\(\Gamma_0(N)\)-optimal
330096.l1	330096l2	\([0, -1, 0, -1004, -11460]\)	\(35969456/1521\)	\(4737537792\)	\([2]\)	\(184320\)	\(0.62105\)