Elliptic curve isogeny class with LMFDB label 17424.bd (Cremona label 17424ba)

• Label: 17424.bd
• Number of curves: $2$
• Conductor: $17424$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Rank

The elliptic curves in class 17424.bd have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 17424.bd has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 17424.2.a.bd

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 17424.bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
17424.bd1	17424ba1	\([0, 0, 0, 0, -58564]\)	\(0\)	\(-1481648585472\)	\([]\)	\(12672\)	\(1.0142\)	\(\Gamma_0(N)\)-optimal	\(-3\)
17424.bd2	17424ba2	\([0, 0, 0, 0, 1581228]\)	\(0\)	\(-1080121818809088\)	\([]\)	\(38016\)	\(1.5635\)		\(-3\)