Elliptic curve isogeny class with Cremona label 30400bv (LMFDB label 30400.br)

• Label: 30400bv
• Number of curves: $3$
• Conductor: $30400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 30400bv have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 30400bv do not have complex multiplication.

Modular form 30400.2.a.bv

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 30400bv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
30400.br3	30400bv1	\([0, -1, 0, 67, -13]\)	\(32768/19\)	\(-19000000\)	\([]\)	\(5184\)	\(0.086119\)	\(\Gamma_0(N)\)-optimal
30400.br2	30400bv2	\([0, -1, 0, -933, 11987]\)	\(-89915392/6859\)	\(-6859000000\)	\([]\)	\(15552\)	\(0.63543\)
30400.br1	30400bv3	\([0, -1, 0, -76933, 8238987]\)	\(-50357871050752/19\)	\(-19000000\)	\([]\)	\(46656\)	\(1.1847\)